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We introduce the adjoint homological Selmer module for an $\textrm {SL}_2$-representation of a knot group, which may be seen as a knot theoretic analogue of the dual adjoint Selmer module for a Galois representation. We then show finitely generated torsion-ness of our adjoint Selmer module, which are widely known as conjectures in number theory, and give some concrete examples.

We introduce mod $l$ Milnor invariants of a Galois element associated to Ihara's Galois representation on the pro-$l$ fundamental group of a punctured projective line ($l$ being a prime number), as arithmetic analogues of Milnor invariants of a pure braid. We then show that triple quadratic (resp. cubic) residue symbols of primes in the rational (resp. Eisenstein) number field are expressed by mod $2$ (resp. mod $3$) triple Milnor invariants of Frobenius elements. For this, we introduce dilogarithmic mod $l$ Heisenberg ramified covering ${\cal D}^{(l)}$ of $\mathbb{P}^1$, which may be regarded as a higher analog of the dilogarithmic function, for the gerbe associated to the mod $l$ Heisenberg group, and we study the monodromy transformations of certain functions on ${\cal D}^{(l)}$ along the pro-$l$ longitudes of Frobenius elements for $l=2,3$., Comment: 33 pages, 1 figure

We study the twisted knot module for the universal deformation of an SL 2 \textrm {SL}_2 -representation of a knot group and introduce an associated L L -function, which may be seen as an analogue of the algebraic p p -adic L L -function associated to the Selmer module for the universal deformation of a Galois representation. We then investigate two problems proposed by Mazur: Firstly we show the torsion property of the twisted knot module over the universal deformation ring under certain conditions. Secondly we compute the L L -function by some concrete examples for 2 2 -bridge knots.

To improve the cycling performance of carbon-coated SiO (SiO–C) as a high-capacity negative electrode material, we have used X-ray absorption fine structure measurements to assess the electronic state of Si and investigate phase changes during charge/discharge cycles. The results suggest that Si 4 + continuously absorbs Li during the charging process, mainly forming Li 4 SiO 4 . Li silicates with a lower valence are also formed. Neutral Si and Si 2 + mainly contribute to Li insertion during the initial charging stage, whereas low-valence oxides like Si 1 + and Si 2 + form during the middle charging stage. The fully charged state contains all Si phase states. These results suggest that during the discharge process, Li is mainly released from composites with Si 2 + -oxidation state, and Li is partially released from Li 4 SiO 4 at a higher voltage forming Si 0 . Si O composites with Si 1 + –Si 3 + reversibly shift to a higher valence state during cycling. We confirmed that Li 4 SiO 4 readily releases Li after long-term cycling, and Si O composites at the end of the cycle change to a higher valence state. The results indicate that disproportionation is a primary factor decreasing cell cycle performance and confirm that it is possible to design LiB cells with improved cycling performance by controlling the disproportionation linked to the structural deterioration of SiO–C.

To improve the cycling performance of the carbon-coated SiO (SiO-C) as a high capacity anode material, the charge–discharge mechanism and the structural changes in the bulk during long-term cycling were investigated by the solid-state nuclear magnetic resonance (NMR). The electron conductivity of the SiO-C was improved following the charging state, whereas the electrical resistivity tended to be low. It suggested that from the beginning of the discharge to its half state (at the low potential side), the silicide reaction is predominant, whereas at the terminal phase of the discharge (at the high potential side), the release of Li from the silicate is predominant. Upon designing a negative cutoff potential of 1.1 V, the cell's cycling performance was checked. The results suggested that during repeated charge-discharge cycling, Li release from the silicate decreased and a disproportionation reaction occurred which produced Si and Li4SiO4. It was confirmed that a part of the cycle performance was improved by designing a battery utilizing the low potential side which is supposed to increase the electron conductivity and suppressed the disproportionation.

Lithium ion batteries for electric vehicle (EV) applications require high energy density and high safety. For this reason, layered oxides such as LiNiCoMnO2 (NCM) and LiNiCoAlO2 (NCA) are selected as positive electrode materials because of their large charge / discharge capacity. In recent years, capacity and energy density have been increasing due to an increase in the Ni content. However, an increase in the Ni content tends to cause heat generation and oxygen release from the crystal structure during charge / discharge, which leads to a decrease in battery safety such as the battery being easily ignited. On the other hand, olivine-type cathode materials such as LiFePO4 (LFP) and LiFeMnPO4 (LFMP) are widely known as highly safe cathode materials that generate less heat and do not cause oxygen release from the crystal structure during charge / discharge. However, these olivine-type materials have smaller charge / discharge capacities and powder densities than layered oxides, and thus have low energy densities and are therefore difficult to apply to batteries for electric vehicles. In this study, we investigated the effects of mixing layered oxides and olivine-type materials to compensate for the advantages and disadvantages of layered oxides and olivine-type materials, and to achieve cathode materials with both high energy density and high safety. As the cathode electrode material, NCM532 was used as a layered oxide, and LFP or LFMP produced by a hydrothermal synthesis method were used as an olivine type material. These materials were mixed at a predetermined weight ratio when preparing the electrode paste. The prepared paste was applied to an Al foil and dried to obtain a mixed electrode of NCM / olivine type material. The mixed state of NCM / olivine type material in the electrode was observed by SEM. As a result, a high dispersion state was obtained regardless of the mixing ratio of both materials. For charge / discharge tests, 50 mAh Laminate cells were prepared using the NCM / olivine type material electrode for cathode and natural graphite for anode. As a result, NCM / LFP mixed electrode showed a slight decrease in energy density due to an increase in the capacity of the 3.1 V region derived from the change in Fe valence as the amount of LFP mixed increased. On the other hand, in the NCM / LFMP mixed electrode, the capacity in the 3.9 V region derived from the change in the Mn valence in LFMP increased as the amount of LFMP mixed increased. Since the Fe content of LFMP was small, the capacity in the 3.1 V region was hardly observed due to the increase in the amount of LFMP. For a safety test, a 2 Ah laminate cells were prepared and an overcharge test was performed. Overcharging was performed up to a voltage of 30 V by applying a current of 20 A. As a result of evaluating the cell using the NCM single electrode, the surface temperature rose to 195.2 oC and the cell was flamed. On the other hand, in the cell using the NCM / LFP electrode, the surface temperature during overcharging was about 50 oC, and although the cell swelled, no leakage or flame occurred. In the case of the cell using the NCM / LFMP electrode, the cell surface temperature increased to 155.4 oC and leakage occured at a weight ratio of 80/20. At the weight ratio of 70/30 or less, the cell surface temperature decreased to around 50 oC, and the cells only swelled and did not flame. In conclusion, we were able to obtain a positive electrode material that has both high safety and high energy density by mixing NCM with an olivine type positive electrode material. In the future, we will consider mixing olivine-type cathode materials with higher energy density oxides such as NCA. Figure 1

The Li pre-doping free cells using tin-phosphate glass (GSPO)-silicon composite anodes and lithium-rich layered oxide (LR-NMC) cathode were developed, in which the irreversible capacity of the cathode was utilized in order to compensate that of the anode. The irreversible capacity was equalized to that of the cathode at a Si/(GSPO + Si) mass ratio, r , of 0.8. The cell using the composite anode of r = 0.8 displayed a discharge capacity of 187 mAh g −1 as the cathode capacity at 30 °C and the 0.1C-rate. The long cycle performance of over 100 charge–discharge cycles was achieved. The cells also showed an excellent high- and low-temperature performance and a good rate performance. A stable performance was observed for over 50 cycles at 60 °C and the 0.5C-rate, and a high capacity of ca. 100 mAh g −1 as the cathode capacity even at −20 °C and the 0.2C-rate. The cell could discharge even at the 10C-rate. Furthermore, the Li pre-doping free cell showed an outstanding safety performance during the nail penetration test. When the 1500 mAh cell using the composite anode was penetrated by a nail, no thermal runaway was observed during the test.

Based on the analogies between knot theory and number theory, we study a deformation theory for SL_2-representations of knot groups, following after Mazur's deformation theory of Galois representations. Firstly, by employing the pseudo-SL_2-representations, we prove the existence of the universal deformation of a given SL_2-representation of a finitely generated group Pi over a field whose characteristic is not 2. We then show its connection with the character scheme for SL_2-representations of Pi when k is an algebraically closed field. We investigate examples concerning Riley representations of 2-bridge knot groups and give explicit forms of the universal deformations. Finally we discuss the universal deformation of the holonomy representation of a hyperbolic knot group in connection with Thurston's theory on deformations of hyperbolic structures., Comment: 25 pages, to appear in Tohoku Math. J; corrected typos

Olivine lithium manganese phosphate (LiMnPO 4 ) becomes research focus because of its high energy density and improved thermal stability. However, its application in lithium ion batteries suffers severely from poor electrochemical activity due to low conductivity and structural instability upon the charge and discharge process. By applying a high-energy ball-milling method we succeed in improving the capacity delivery and rate capability. LiMnPO 4 materials ball-milled without or with acetylene black are able to deliver a high capacity of 135 and 127 mAh g −1 , respectively, more than 50% greater than the pristine one. Particularly, the latter also shows an improved discharge plateau and stable cyclability. High-energy synchrotron radiation X-ray diffraction (XRD), scanning electron microscopy (SEM), Raman spectroscopy, laser particle analysis, and galvanostatic charge and discharge are employed to understand the effect of ball-milling on the LiMnPO 4 material.

Lithium vanadium metasilicate (LiVSi 2 O 6 ) with pyroxene structure has been exploited as an electrode material for Li-ion batteries. Galvanostatic charge and discharge tests show that LiVSi 2 O 6 is able to deliver a capacity of 85 mAh g −1 at 30 °C, and a high capacity of 181 mAh g −1 at 60 °C. The high capacity is believed to be due to the reactions of V 3+ /V 4+ and V 2+ /V 3+ redox couples, accompanied by the excess 0.42 Li + insertion into the lattice forming a Li-rich phase Li 1.42 VSi 2 O 6 . High-energy synchrotron XRD combined with the Rietveld refinement analysis confirms that the electrochemical delithiation–lithiation reaction proceeds by a single phase redox mechanism with an overall volume variation of 1.9% between LiVSi 2 O 6 and its delithiated state, indicating a very stable framework of LiVSi 2 O 6 for Li + ions extraction–insertion.

Well-crystallized LiFePO 4 nanoparticles have been directly synthesized in a short time via hydrothermal process in the presence of organic acid, e.g. citric acid or ascorbic acid. These acid-mediated LiFePO 4 products exhibit a phase-pure and nanocrystal nature with size about 50–100 nm. Two critical roles that the organic acid mediator plays in hydrothermal process are recognized and a rational mechanism is explored. After a post carbon-coating treatment at 600 °C for 1 h, these mediated LiFePO 4 materials show a high electrochemical activity in terms of reversible capacity, cycling stability and rate capability. Particularly, LiFePO 4 mediated by ascorbic acid can deliver a capacity of 162 mAh g −1 at 0.1 C, 154 mAh g −1 at 1 C, and 122 mAh g −1 at 5 C. The crystalline structure, particle morphology, and surface microstructure were characterized by high-energy synchrotron X-ray diffraction (XRD), transmission electron microscopy (TEM) and scanning electron microscopy (SEM), and Raman spectroscopy, respectively. And the electrochemical properties were thoroughly investigated by galvanostatic test and electrochemical impedance spectroscopy (EIS).

It was revealed that the metastable region, in which liquid phase epitaxy (LPE) of GaN single crystals proceeds without the generation of polycrystals, expands with growth temperature in the Na flux method. The metastable region appears when LPE growth proceeds at temperatures above 1073 K, although generation of polycrystals inevitably occurs on a crucible at temperatures less than 1073 K. The highest growth rate of 14 μm/h in a small experimental setup was achieved at a temperature of 1163 K with a nitrogen pressure of 5.5 MPa due to complete suppression of the growth of polycrystals on a crucible, even though the supersaturation at this condition reached a fairly high level. Also, an LPE crystal with a flat surface could easily be obtained under high-temperature conditions.

The detailed structural change in the charge–discharge process was investigated for the 20 mol% aluminum-substituted α-nickel hydroxide by using high-energy synchrotron X-ray diffraction (XRD), X-ray absorption fine structure (XAFS) and transmission electron microscopy (TEM) analysis. The 20 mol% aluminum-substituted α-nickel hydroxide showed the α-Ni(OH) 2 /γ-NiOOH phase transformation in the charge–discharge process. The structural refinement has been done successfully on the basis of two phase models of the ideal phases and the fault ones, including the occupation sites for the potassium ions and H 2 O (OH − ) molecules. The substituted aluminum ions were situated on both nickel sites and 18h sites in the interlayer. The α-Ni(OH) 2 structure would be stabilized by the presence of the aluminum ions on the 18h sites. The α-Ni(OH) 2 phases were transformed to the β-Ni(OH) 2 phases after 50 cycles because the aluminum ions on the 18h sites would be migrated from the bulk to the surface.

Under partial charge–discharge cycling conditions at a state of charge (SoC) of 50–70%, a greater effect on the suppression of the memory effect, which occurs in rechargeable alkaline batteries containing a Ni-electrode, was observed using conductive materials such as nano-sized Co(OH) 2 and CoO powders in the Ni-electrode. The nano-sized Co(OH) 2 powder, prepared by the reverse micelle method, consisted of approximately 15–60 nm spherical-shaped particles. The Ni–Cd cells containing approximately 15- or 20-nm-sized Co(OH) 2 powder and 18 nm CoO powder in the Ni-electrode did not show any memory effect after a 150-cycle partial charge–discharge cycling test, and γ-NiOOH, which is mainly the origin of the memory effect, was not detected in the Ni-electrode, whereas the Ni–Cd cell containing the same content of 500 nm Co(OH) 2 powder and 18 nm CoO in the Ni-electrode showed the memory effect. The nano-sized Co(OH) 2 powder could be more homogeneously dispersed in the Ni-electrode when compared to the 500 nm powders and might develop a superior electro-conductive network between the Ni(OH) 2 particles.

We succeeded in growing a GaN single crystal substrate with diameter of about two inches using the Na flux method. Our success is due to the development of a new apparatus for growing large GaN single crystals. The crystal grown in this study has a low dislocation density of 2.3×105 (cm-2), The secondary ion mass spectrometry (SIMS) technique demonstrates that the Na element is difficult to be taken in the crystal in both the + and – c directions, resulting in a Na concentration of 4.2 × 1014 (cm-3) in the crystal. Our success in growing a two-inch GaN substrate with a low impurity content and low dislocation density should pave the way for the Na flux method to become a practical application.

We found that a carbon additive could suppress the unfavorable generation of polycrystals in a crucible without reduction in the yield of GaN in the Na flux method. The suppression of polycrystals due to the effect of carbon significantly increased the growth rate of liquid phase epitaxy (LPE), which has been the biggest problem of the Na flux LPE, and enabled an increase in the growth rate above 20 μm/h. A 3 mm-thick 2 in GaN crystal was obtained for the first time. In addition, the carbon additive was found to have another effect in that the nonpolar face could be widely developed. SIMS measurements revealed that carbon added into a Ga–Na mixed melt was hardly taken into LPE crystals, although carbon did have some favorable effects.

We introduce a multiple generalization of the tame symbol, called {\em polysymbols}, associated to meromorphic functions on a Riemann surface as the Massey products in Deligne cohomology, and also give a geometric construction of polysymbols using Chen's iterated integrals. We then deduce some basic properties of polysymbols using our holonomy formula, and show that trivializations of polysymbols give variations of mixed Hodge structure.

The detailed phase transformation in the charge-discharge process for the nickel hydroxide electrode have been examined by using the high-energy synchrotron X-ray absorption fine structure (XAFS) and X-ray diffraction (XRD). The structural refinement for the β-Ni(OH)2 and the β-NiOOH have been done successfully on the basis of two phase models of the ideal and fault phases. At 0% of SOC, it was found that the sample consisted of 80% of the ideal β-Ni(OH)2 phases and 20% of the fault ones. At 100% of SOC, the ideal and fault β-Ni(OH)2 phases were transformed to the ideal and fault β-NiOOH phases, respectively. It was found that the fault phases contained a larger amount of intercalated potassium ions and H2O (OH−) than the ideal ones. At 150% of SOC, the only ideal β-NiOOH phases was transformed to the ideal γ-NiOOH phases, accompanied by further intercalation of the potassium ions and H2O (OH−) into the interlayer

Ihara initiated to study a certain Galois representation which may be seen as an arithmetic analogue of the Artin representation of a pure braid group. We pursue the analogies in Ihara theory further, following after some issues and their inter-relations in the theory of braids and links such as Milnor invariants, Johnson homomorphisms, Magnus-Gassner cocycles and Alexander invariants, and study relations with arithmetic in Ihara theory., Comment: 66pages, to appear in Publ. Res. Inst. Math. Sci., corrected typos

We observed the memory effect, the working voltage lowering, which occurred due to the repeated partial charge-discharge cycling of a Ni-capacity-limited alkaline cell, for example 50–70% state of charge, and γ-NiOOH in the Ni electrode was identified as the cause of the memory effect. During this condition, γ-NiOOH is proposed to be formed by partial overcharging due to the heterogeneity of the conductive materials such as cobalt compounds in the Ni electrode. Using nano-sized conductive materials homogeneously dispersed in the electrode leads to a significant effect on the suppression of the memory effect occurring due to the repeated partial charge-discharge cycling.

Following the analogy between primes and knots, we give an arithmetic analogue of a theorem by E. Hironaka on the Alexander stratification in the character variety of a knot group.

The effect of the addition of Li or Ca to Ga–Na melt on the promotion of nitrogen dissolution was examined quantitatively in the growth of GaN single crystals using the sodium flux method. The addition of Li or Ca to Ga–Na melt increased both the solubility of solid GaN and that of gaseous nitrogen against the solution. The increase in the solubility of gaseous nitrogen seems to be caused by additives having a high binding energy with nitrogen. We measured the solubility of GaN and that of gaseous nitrogen against Ga–Na, Ga–Na–Li and Ga–Na–Ca melt in this study. On the basis of these data, we clarified the relationship between the N/Ga ratio in the solution and the coloration of GaN crystals grown in each system, and between changes in the yield of GaN and the absolute value of supersaturation.

In the growth of GaN single crystal using the Na flux method, we succeeded in clarifying the role of Na in promoting nitrogen dissolution in the Ga-Na melt system above 900 K. At the gas-liquid interface of high temperature Ga-Na melt, Na functions to ionize the nitrogen gas. The ionization of the nitrogen gas results in drastic increase of nitrogen dissolution in the melt. In consequence, these synthesize GaN single crystals easily. On the other hand, the addition of a minor amount of Ca or Li to the Ga-Na melt system also increases the nitrogen dissolution. However, the additives function to maintain the nitrogen dissolved in the Ga-Na melt, which results in drastic increase in the nitrogen concentration. In the present study, we report the solubility of GaN in the Ga-Na system and the threshold pressure of nitrogen gas to grow GaN. On the basis of these data, we propose a growth mechanism of GaN and the role of additives to maintain nitrogen.

The dependency of LPE growth rate and dislocation density on supersaturation in the growth of GaN single crystals in the Na flux was investigated. When the growth rate was low during the growth of GaN at a small value of supersaturation, the dislocation density was much lower compared with that of a substrate grown by the Metal Organic Chemical Vapor Deposition method (MOCVD). In contrast, when the growth rate of GaN was high at a large value of supersaturation, the crystal was hopper including a large number of dislocations. The relationship between the growth conditions and the crystal color in GaN single crystals grown in Na flux was also investigated. When at 800 °C the nitrogen concentration in Na–Ga melt was low, the grown crystals were always tinted black. When the nitrogen concentration at 850 °C was high, transparent crystals could be grown.

Following the analogy between primes and knots, we introduce the refined Milnor invariants for prime numbers and establish their connection with certain Massey products in Galois cohomology. This generalizes the well-known relation between the power residue symbol and cup product and gives a cohomological interpretation of L. Redei's triple symbol.

We investigated the threshold pressure necessary for heterogeneous nucleation of GaN using pure nitrogen gas and nitrogen gas mixed with ammonia in the Na-flux method. In our investigation, we found the appropriate pressure region for nucleating GaN and growing GaN seed crystals without additional heterogeneous nucleation. This study revealed that the threshold pressure to nucleate GaN decreases as the ratio of ammonia increases. We also succeeded in reducing the nucleation threshold pressure from 30 to 10 atm by using nitrogen gas with 25–40% ammonia gas instead of pure nitrogen gas. We confirmed that seed growth without additional nucleation is possible in both pure nitrogen and nitrogen gas mixed with ammonia at pressures below those required for nucleation.

A new wet limestone−gypsum process for flue gas desulfurization (FGD) has been developed. The main difference compared to a conventional wet FGD process is the ability of the new process to utilize granular limestone directly as a desulfurizing reagent. Thus, the pulverizing of limestone, which causes power consumption, can be avoided. The performance of the wet FGD process using granular limestone was confirmed to be equal to or higher than that of a conventional process in various tests. Tests were also performed in a 2000 m3Normal/h demonstration plant introducing actual flue gas of various types of coals at Matsuura Thermal Power Station of the Electric Power Development Co., Ltd. (EPDC) in Japan. It was also confirmed that the desulfurization performance of the granular limestone FGD process was not decreased by aluminum−fluorine-containing compounds in the absorbing slurry as much as in the pulverized limestone case. In this new wet FGD process, gypsum quality was also higher than that in a conventi...

We introduce mod 3 triple Milnor invariants and triple cubic residue symbols for certain primes of the Eisenstein number field $\mathbb{Q}(\sqrt{-3})$, following the analogies between knots and primes. Our triple symbol generalizes both the cubic residue symbol and R\'{e}dei's triple symbol, and describes the decomposition law of a prime in a mod 3 Heisenberg extension of degree 27 over $\mathbb{Q}(\sqrt{-3})$ with restricted ramification, which we construct concretely in the form similar to R\'{e}dei's dihedral extension over $\mathbb{Q}$. We also give a cohomological interpretation of our symbols by triple Massey products in Galois cohomology., Comment: 42 pages. The previous version entitled "Arithmetic Milnor invariants and multiple power residue symbols in number fields" by F. Amano and M. Morishita contained some mistakes concerning Theorem 2.8. This is a new version for the Eisenstein number field, which revises largely the previous one, with the collaboration of Y. Mizusawa. To appear in Research in Number Theory

We study the asymptotic distribution of S-integral points on affine homogeneous spaces in the light of the Hardy–Littlewood property introduced by Borovoi and Rudnick. We introduce the S-Hardy–Littlewood property for affine homogeneous spaces defined over an algebraic number field and a finite set S of places of the base field. We work with the adelic harmonic analysis on affine algebraic groups over a number field to determine the asymptotic density of S-integral points under congruence conditions. We give some new examples of strongly or relatively S-Hardy–Littlewood homogeneous spaces over number fields. As an application, we prove certain asymptotically uniform distribution property of integral points on an ellipsoid defined by a totally positive definite tenary quadratic form over a totally real number field.

We succeeded in growing a GaN single crystal substrate with diameter of about two inches using the Na flux method. Our success is due to the development of a new apparatus for growing large GaN single crystals. The crystal grown in this study has a low dislocation density of 2.3×105 cm-2. The secondary ion mass spectrometry (SIMS) technique demonstrates that the Na element is difficult to be taken in the crystal in both the "+" and "-" c directions, resulting in a Na concentration of 4.2×1014 cm-3 in the crystal. Our success in growing a two-inch GaN substrate with a low impurity content and low dislocation density should pave the way for the Na flux method to become a practical application.

In 1939, L. Rédei introduced a certain triple symbol in order to generalize the Legendre symbol and Gauss' genus theory. Rédei's triple symbol $[a_1,a_2, p]$ describes the decomposition law of a prime number $p$ in a certain dihedral extension over $\mathbb{Q}$ of degree 8 determined by $a_1$ and $a_2$. In this paper, we show that the triple symbol $[-p_1,p_2, p_3]$ for certain prime numbers $p_1, p_2$ and $p_3$ can be expressed as a Fourier coefficient of a modular form of weight one. For this, we employ Hecke's theory on theta series associated to binary quadratic forms and realize an explicit version of the theorem by Weil-Langlands and Deligne-Serre for Rédei's dihedral extensions. A reciprocity law for the Rédei triple symbols yields certain reciprocal relations among Fourier coefficients.

Let G be a connected linear algebraic group and X an algebraic variety, both defined over Q, the field of rational numbers. Suppose that G acts on X transitively and the action is defined over Q. Suppose that the set of rational points X(Q) is non-empty. Choosing x ∈ X(Q) allows us to identify G/Gx and X as varieties over Q, there Gx is the stabilizer of x.

We introduce a nilpotent Hurewicz homomorphism for a topological manifold, following the Lie algebra method in nilpotent class field theory for local and number fields by H. Koch et al. Using Labute-Anick’s results on the determination of the Lie algebra attached to the lower central series of a group, we present explicitly nilpotent class field theory for some two and three dimensional manifolds.

We propose an approach to study non-Abelian Iwasawa theory, using the idea of Johnson homomorphisms in low dimensional topology. We introduce arithmetic analogues of Johnson homomorphisms/maps, called the p-Johnson homomorphisms/maps, associated to the Zassenhaus filtration of a pro-p Galois group over a Z_p-extension of a number field. We give their cohomological interpretation in terms of Massey products in Galois cohomology., Comment: 38 pages, to appear in J. of Algebra, changed title from "p-Johnson homomorphisms in non-Abelian Iwasawa theory", added references in section 5, corrected typos