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Your search keyword '"Ibarra, Dionne"' showing total 43 results
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43 results on '"Ibarra, Dionne"'

1. Lambda lengths in The figure eight knot complement

Author

Howie, Joshua A., Ibarra, Dionne, Mathews, Daniel V., and Su, Lecheng

Subjects
Mathematics - Geometric Topology, 57K32 (Primary) 15A66, 53C27, 11R04 (Secondary)
Abstract

In the complete hyperbolic structure on the complement of the figure eight knot, we determine the set of lambda lengths from the maximal cusp to itself. Using the correspondence between spinors and spin-decorated horospheres, we show that these lambda lengths are precisely the Eisenstein integers, up to multiplication by a unit. We also show that the inter-cusp distances from the maximal cusp to itself are precisely the norms of Eisenstein integers., Comment: 14 pages, 4 figures

Published
2024

2. A Study of Gram Determinants in Knot Theory

Author

Ibarra, Dionne and Montoya-Vega, Gabriel

Subjects
Mathematics - Geometric Topology, Primary: 57M25 Secondary: 57M27
Abstract

Historically originated as a sub-field of topology, knot theory is an active area of mathematical investigation that has strong connections with a diverse set of scientific fields such as algebra, biology, and statistical mechanics. A popular and important concept in linear algebra, Gram determinants enjoy a connection with the mathematical theory of knots. In this article, we expose this concept and present several types of Gram determinants in what can be considered as a survey of the current Gram determinants of interest to knot theorists; examples are included to illustrate the definitions. In particular, we pay special attention to a recently defined determinant from a M\"obius band and we further study its structure. At the end, some speculation is presented regarding the closed formula for the Gram determinant of type $(Mb)_1$, a problem that arouses serious interest among knot theorists., Comment: 17 pages, 71 figures

Published
2024

3. A lower bound for the volumes of modular link complements

Author

Hui, Connie On Yu, Ibarra, Dionne, and Migueles, José Andrés Rodríguez

Subjects
Mathematics - Geometric Topology, Mathematics - Dynamical Systems, 57K10, 57K32 (primary) 37D40, 37E35 (secondary)
Abstract

Every finite collection of oriented closed geodesics in the modular surface has a canonically associated link in its unit tangent bundle coming from the periodic orbits of the geodesic flow. We study the volume of the associated link complement with respect to its unique complete hyperbolic metric. We provide the first lower volume bound that is linear in terms of the number of distinct exponents in the code words corresponding to the collection of closed geodesics., Comment: 20 pages, 8 figures

Published
2024

4. The Temperley-Lieb Algebra and the Artin Braid Group

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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5. Long Exact Sequence of Khovanov Homology and Torsion

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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6. Variations on Catalan Connections and the Children Pairing Game

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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7. Symmetrizers of Finite Groups and the Jones-Wenzl Idempotent

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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8. Goeritz and Seifert Matrices

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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9. From Fox 3-Coloring to the Yang-Baxter Operator and Its Homology

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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10. The Jones Polynomial and Kauffman Bracket Polynomial

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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11. History of Knot Theory from Gauss to Jones

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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12. The HOMFLYPT and the Two-Variable Kauffman Polynomial

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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13. The Witten-Reshetikhin-Turaev Invariants of 3-Manifolds

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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14. Khovanov Homology: A Categorification of the Jones Polynomial

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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15. Spin Structure and the Framing Skein Module of Links in 3-Manifolds

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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16. Gram Determinants of Type A and Generalized Type A

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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17. History of Knot Theory from Ancient Times to Gauss and His Student Listing

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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18. The Kauffman Bracket Skein Module and Algebra of Surface I-Bundles

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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19. Gram Determinants of Type B and Type Mb

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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20. Multiplicative Structure of the Kauffman Bracket Skein Algebra of the Thickened T-Shirt

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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21. Basics of Skein Modules

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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22. Plucking Polynomial of Rooted Trees and Its Use in Knot Theory

Author

Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, Weeks, Deborah, Berestycki, Nathanaël, Series Editor, Casacuberta, Carles, Series Editor, Greenlees, John, Series Editor, MacIntyre, Angus, Series Editor, Sabbah, Claude, Series Editor, Süli, Endre, Series Editor, Przytycki, Józef H., Bakshi, Rhea Palak, Ibarra, Dionne, Montoya-Vega, Gabriel, and Weeks, Deborah

Published
2024
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23. On a new Gram determinant from the M\'obius band

Author

Ibarra, Dionne and Montoya-Vega, Gabriel

Subjects
Mathematics - Geometric Topology, 57K10 (Primary), 57K31 (Secondary)
Abstract

Gram determinants earned traction among knot theorists after E. Witten's presumption about the existence of a 3-manifold invariant connected to the Jones polynomial. Triggered by the creation of such an invariant by N. Reshetikhin and V. Turaev, several mathematicians have explored this line of research ever since. Gram determinants came into play by W. B. Raymond Lickorish's skein theoretic approach to the invariant. The construction of different bilinear forms is possible through changes in the ambient surface of the Kauffman bracket skein module. Hence, different types of Gram determinants have arisen in knot theory throughout the years; some of these determinants are discussed here. In this article, we introduce a new version of such a determinant from the M\"obius band and prove some important results about its structure. In particular, we explore its connection to the annulus case and factors of its closed formula., Comment: 15 pages, comments welcomed

Published
2023
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24. Jones-Wenzl Idempotents in the Twisted $I$-bundle over the M\'obius band

Author

Ibarra, Dionne

Subjects
Mathematics - Geometric Topology, 57K10 (Primary), 57K31 (Secondary)
Abstract

The Jones-Wenzl idempotent plays a vital role in quantum invariants of $3$-manifolds and the colored Jones polynomial; it also serves as a useful tool for simplifying computations and proving theorems in knot theory. The relative Kauffman bracket skein module (RKBSM) for surface $I$-bundles and manifolds with marked boundaries have a well understood algebraic structure due to the work of J. H. Przytycki and T. T. Q. L\^e. It has been well documented that the RKBSM of the $I$-bundle of the annulus and the twisted $I$-bundle over the M\"obius band have distinct algebraic structures coming from the $I$-bundle structures. This paper serves as an introduction to studying the trace of Jones-Wenzl idempotents in the Kauffman bracket skein module (KBSM) of the twisted $I$-bundle of unorientable surfaces. We will give various results on Jones-Wenzl idempotents in the KBSM of the twisted $I$-bundle over the M\"obius band when it is closed through the crosscap of the M\"obius band. We will also uncover analog properties of Jones-Wenzl idempotents in the KBSM of the twisted $I$-bundle over the M\"obius band with the preservation of the $I$-bundle structure that differ from the KBSM of $Ann \times I$., Comment: 20 pages, comments welcomed

Published
2023

25. A note on a short proof of the parallelizability of orientable $3$-manifolds

Author

Ibarra, Dionne

Subjects
Mathematics - Geometric Topology, 57K10 (Primary), 57K50, 57R25 (Secondary)
Abstract

We survey, complete, and modify a proof, involving knot theory, of Stiefel's theorem that all orientable $3$-manifolds are parallelizable. The completion of the proof is done by using the relationship between the tangent bundle and normal bundle of manifolds with non-trivial boundary and on stably parallelizable and parallelizable manifolds. We end with a remark on $7$-manifolds and present J. Korba\v{s}' example of a non-parallelizable $7$-manifold., Comment: 7 pages, 1 figure, comments welcomed

Published
2022

34. Basics of Skein Modules

Author

Przytycki, Józef H., primary, Bakshi, Rhea Palak, additional, Ibarra, Dionne, additional, Montoya-Vega, Gabriel, additional, and Weeks, Deborah, additional

Published
2023
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40. Goeritz and Seifert Matrices

Author

Przytycki, Józef H., primary, Bakshi, Rhea Palak, additional, Ibarra, Dionne, additional, Montoya-Vega, Gabriel, additional, and Weeks, Deborah, additional

Published
2023
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42. A new Gram determinant from the Möbius band.

Author

Ibarra, Dionne and Montoya-Vega, Gabriel

Subjects
*BILINEAR forms, *MATHEMATICIANS, *POLYNOMIALS, *THEORISTS
Abstract

Gram determinants earned traction among knot theorists after Witten's presumption about the existence of a 3-manifold invariant connected to the Jones polynomial. Triggered by the creation of such an invariant by Reshetikhin and Turaev, several mathematicians have explored this line of research ever since. Gram determinants came into play by Lickorish's skein theoretic approach to the invariant. The construction of different bilinear forms is possible through changes in the ambient surface of the Kauffman bracket skein module. Hence, different types of Gram determinants have arisen in knot theory throughout the years; some of these determinants are discussed here. In this paper, we introduce a new version of such a determinant from the Möbius band and prove some important results about its structure. In particular, we explore its connection to the annulus case and factors of its closed formula. [ABSTRACT FROM AUTHOR]

Published
2024
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