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Bousfield introduced an algebraic category of modules that reflects the structure detected by p-localized complex topological K-theory. He constructed, for any module M in this category, a natural 4-term exact sequence 0 → M → U M → U M → M ⊗ Q → 0 , where U denotes the co-free functor, right adjoint to the forgetful functor to Z (p) -modules. Clarke et al. identified the objects of Bousfield's category as the 'discrete' modules for a certain topological ring A, obtained as a completion of the polynomial ring Z (p) [ x ] , and simplified the construction of the Bousfield sequence in this context. We introduce the notion of 'cobasically discrete' R-modules as a clarification of the Clarke et al. modules, noting that these correspond to comodules over the coalgebra that R is dual to. We study analogues of the Bousfield sequence for other polynomial completion rings, noting a variety of behaviour in the last term of the sequence. [ABSTRACT FROM AUTHOR]

The k-Cauchy–Fueter complex in quaternionic analysis was generalized to the Heisenberg group in a previous paper (Ren et al., in Adv Appl Clifford Algebras 30(2): Paper No. 20, 2020). But it is not known whether this differential complex is exact or not. In this paper, we apply the Penrose transform (the twistor method) to a double fibration of homogeneous spaces of SO (2 N , C) to prove its exactness on the Heisenberg group. [ABSTRACT FROM AUTHOR]

Let X be a Hopf manifold with non-Abelian fundamental group and E be a holomorphic vector bundle over X, with trivial pull-back to ℂn − {0}. The authors show that there exists a line bundle L over X such that E ⊗ L has a nowhere vanishing section. It is proved that in case dim(X) ≥ 3, π*(E) is trivial if and only if E is filtrable by vector bundles. With the structure theorem, the authors get the cohomology dimension of holomorphic bundle E over X with trivial pull-back and the vanishing of Chern class of E. [ABSTRACT FROM AUTHOR]

The paper deals with the normal extensions of cancellative commutative semigroups and the Toeplitz algebras for those semigroups. By the Toeplitz algebra for a semigroup S one means the reduced semigroup C*-algebra Cr*(S). We study the normal extensions of cancellative commutative semigroups by the additive group ℤn of integers modulo n. Moreover, we assume that such an extension is generated by one element. We present a general method for constructing normal extensions of semigroups which contain no non-trivial subgroups. The Grothendieck group for a given semigroup and the group of all integers are involved in this construction. Examples of such extensions for the additive semigroup of non-negative integers are given. A criterion for a normal extension generated by an element to be isomorphic to a numerical semigroup is given in number-theoretic terms. The results concerning the Toeplitz algebras are the following. For a cancellative commutative semigroup S and its normal extension L generated by one element, there exists a natural embedding the semigroup C*-algebra Cr*(S) into Cr*(L). The semigroup C*-algebra Cr*(L) is topologically ℤn-graded. The results in the paper are announced without proofs. [ABSTRACT FROM AUTHOR]

In this paper, the notion of (short) quasi-exact sequence of S-acts is introduced. We study the behaviour of quasi-exact sequences in regard to some algebraic properties of S-acts including principal weak injectivity, principal weak flatness, regularity and torsion freeness. Moreover, some results concerning commutative diagrams of modules are generalized to acts over monoids. [ABSTRACT FROM AUTHOR]

A V-cycle multigrid method for the Hellan-Herrmann-Johnson (HHJ) discretization of the Kirchhoff plate bending problems is developed in this paper. It is shown that the contraction number of the V-cycle multigrid HHJ mixed method is bounded away from one uniformly with respect to the mesh size. The uniform convergence is achieved for the V-cycle multigrid method with only one smoothing step and without full elliptic regularity assumption. The key is a stable decomposition of the kernel space which is derived from an exact sequence of the HHJ mixed method, and the strengthened Cauchy Schwarz inequality. Some numerical experiments are provided to confirm the proposed V-cycle multigrid method. The exact sequences of the HHJ mixed method and the corresponding commutative diagram is of some interest independent of the current context. [ABSTRACT FROM AUTHOR]

This paper examines special metrics on compact complex manifolds, and it is notably focused on the notion of super strong Kähler with torsion metric. This condition is related to the strong Kähler with torsion one in the same manner as the strongly Gauduchon condition is related to the Gauduchon one. Moreover, we provide sufficient and necessary conditions so that every strong Kähler with torsion metric on a compact complex manifold is in fact super strong Kähler with torsion. We prove that these conditions are verified on compact complex manifolds satisfying $$\partial \overline{\partial }$$ -lemma but not on 6-dimensional compact complex nilmanifolds. [ABSTRACT FROM AUTHOR]

We study the Bredon-Illman cohomology with local coefficients for a G-space X in the case of G being a totally disconnected, locally compact group. We prove that any short exact sequence of equivariant local coefficients systems on X gives a long exact sequence of the associated Bredon-Illman cohomology groups with local coefficients. [ABSTRACT FROM AUTHOR]

Higher homotopy of graphs has been defined in several articles. In Dochterman (Hom complexes and homotopy theory in the category of graphs. arXiv math/0605275 v2,28/09/2006, ), the authors asked for a companion homology theory. We define such a theory for the category of unoriented reflexive graphs; it exhibits a long exact sequence for a pair of graphs ( G, A), satisfies an excision property and a Hurewicz theorem. This allows us to compute the top homology of the graphical n-spheres showing that the theory is not trivial and is able to detect n-dimensional holes in a graph. The long-term objective is to compare the homotopy of the topological and graphical spheres. [ABSTRACT FROM AUTHOR]

We formulate and prove a “five lemma”, which unifies two independent generalizations of the classical five lemma in an abelian category: the five lemma in a (modular) semi-exact category in the sense of M. Grandis, and the five lemma in a pointed regular protomodular category in the sense of D. Bourn. [ABSTRACT FROM AUTHOR]

The paper establishes a relation between exact sequences, parametric finite elements, and perfectly matched layer (PML) techniques. We illuminate the analogy between the Piola-like maps used to define parametric H-, H(curl)-, H(div)-, and L-conforming elements, and the corresponding PML complex coordinates stretching for the same energy spaces. We deliver a method for obtaining PML-stretched bilinear forms (constituting the new weak formulation for the original problem with PML absorbing boundary layers) directly from their classical counterparts. [ABSTRACT FROM AUTHOR]

We study the homology structure of the filtration of the space of self-adjoint operators by the multiplicity of the ground state. We consider only operators acting on a finite-dimensional complex or real Hilbert space, but infinite-dimensional generalizations are easy to guess. [ABSTRACT FROM AUTHOR]

In this work, we study the special properties of the equivariant singular cohomology of a G-space X, where G is a totally disconnected, locally compact group. We prove that any short exact sequence of coefficient systems for G, over a ring R, gives a long exact sequence of the associated equivariant singular cohomology modules. We establish the relationship between the ordinary singular cohomology modules and the equivariant singular cohomology modules with the natural contravariant coefficient system. Moreover, under some conditions, we give an isomorphism of the equivariant singular cohomology modules of the G-space X onto the ordinary singular cohomology modules of the orbit space X/ G. [ABSTRACT FROM AUTHOR]

We investigate exactness of long sequences of homology semimodules associated to Schreier short exact sequences of chain complexes of semimodules. [ABSTRACT FROM AUTHOR]

For ap-adic hyperplane arrangement in a vector spaceV, we consider a local system of De Shalit on the Bruhat-Tits building ofPGL(V). We express this local system in terms of Orlik-Solomon algebras, and calculate its cohomology in the case where the arrangement is finite. [ABSTRACT FROM AUTHOR]

Here we show the existence of a rank 2 holomorphic vector bundleE on C2∖{0} without any holomorphic rank 1 subsheaf. Hence, contrary to the algebraic case, there are open subsets of dimension 2 Stein manifolds with holomorphic vector bundles which are not filtrable in any weak sense. [ABSTRACT FROM AUTHOR]

In the connected case, we compute explicity thef-localization (in the sense of [3]) for the class of mapsZ(n)↪Z in which the cofibre is a wedge of spheres. We have an analogous result over the rationals where the cofibre is arbitrary. [ABSTRACT FROM AUTHOR]

We present a sheaf-theoretic setting for convolutional codes in that coherent sheaves (over a projective line) play the same role as finite-dimensional linear spaces in the theory of block codes. Using coherent sheaves (and their cohomologies), we give natural straightforward proofs of the main results on the structural properties of convolutional codes. [ABSTRACT FROM AUTHOR]

Let K be a field of characteristic 2 and let V be a vector space of dimension 2 m over K. Let f be a non-degenerate alternating bilinear form defined on V × V. The symplectic group Sp(2 m, K) acts on the exterior powers Λ k V for 0 ≤ k.≤ 2 m There is a contraction map ∂ defined on the exterior algebra Λ, which commutes with the Sp(2 m, K) action and satisfies ∂2 = 0 and ∂(Λ k V) ≤ Λ k−1 V We prove that ∂(Λ k V)= ker ∂ ∩ Λ k−1 V except when k= m+2. In the exceptional case, ∂(Λ m+2 V) has codimension 2m in ker ∂ ∩ Λ m V and we show that the quotient module ker ∂ ∩ Λ m V/∂ ∩ Λ m+2 V is a spin module for Sp(2 m,K). When K is algebraically closed, we show that this spin module occurs with multiplicity 1 in Λ m V and multiplicity 0 in all other components of Λ V. [ABSTRACT FROM AUTHOR]