논문KCI 등재
Torsion in Homology of Dihedral Quandles of Even Order
경북대학교 자연과학대학 수학과|2020.06|Kyungpook Mathematical Journal|제60권 제2호|pp. 279-288|DOI 10.5666/KMJ.2020.60.2.279
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
Niebrzydowski and Przytycki conjectured that the torsion of rack and quandle homology of a dihedral quandle of order 2k is annihilated by k, unless k = 2t for t > 1. We partially prove this conjecture.
Abstract
Niebrzydowski and Przytycki conjectured that the torsion of rack and quandle homology of a dihedral quandle of order 2k is annihilated by k, unless k = 2t for t > 1. We partially prove this conjecture.
참고문헌 (19)
- N. Andruskiewitsch, "From racks to pointed Hopf algebras", Adv. Math, 178(2), pp.177~243 (2003)
- J. S. Carter, "Extensions of quandles and cocycle knot invariants", J. Knot Theory Ramifications, 12(6), pp.725~738 (2003)
- J. S. Carter, "Cocycle knot invariants, quandle extensions, and Alexander matrices, Low-dimensional topology of tomorrow (Japanese) (Kyoto, 2002)", Surikaisekikenkyusho Kokyuroku, 1272, pp.12~35 (2002)
- J. S. Carter, "Quandle cohomology and state-sum invariants of knotted curves and surfaces", Trans. Amer. Math. Soc, 355(10), pp.3947~3989 (2003)
- F. Clauwens, "The algebra of rack and quandle cohomology", J. Knot Theory Ramifications, 20(11), pp.1487~1535 (2011)
- P. Etingof, "On rack cohomology", J. Pure Appl. Algebra, 177(1), pp.49~59 (2003)
- R. Fenn, "Trunks and classifying spaces", Appl. Categ. Structures, 3(4), pp.321~356 (1995)
- D. Joyce, "A classifying invariant of knots, the knot quandle", J. Pure Appl. Algebra, 23(1), pp.37~65 (1982)
- R. A. Litherland, "The Betti numbers of some finite racks", J. Pure Appl. Algebra, 178(2), pp.187~202 (2003)
- S. V. Matveev, "Distributive groupoids in knot theory", (Russian) Mat. Sb. (N.S.), 119(161), pp.78~88 (1982)
- M. Niebrzydowski, "Homology of dihedral quandles", J. Pure Appl. Algebra, 213(5), pp.742~755 (2009)
- M. Niebrzydowski, "Homology operations on homology of quandles", J. Algebra, 324(7), pp.1529~1548 (2010)
- T. Nosaka, "On homotopy groups of quandle spaces and the quandle homotopy invariant of links", Topology Appl, 158(8), pp.996~1011 (2011)
- T. Nosaka, "On quandle homology groups of Alexander quandles of prime order", Trans. Amer. Math. Soc, 365(7), pp.3413~3436 (2013)
- J. H. Przytycki, "The torsion of a finite quasigroup quandle is annihilated by its order", J. Pure Appl. Algebra, 219(10), pp.4782~4791 (2015)
- J. H. Przytycki, "Annihilation of torsion in homology of finite m-AQ quandles", J. Knot Theory Ramifications, 25(12), pp.16~ (2016)
- S. Y. Yang, "Extended quandle spaces and shadow homotopy invariants of classical links", J. Knot Theory Ramifications, 26(3), pp.13~ (2017)
- S. Y. Yang, "Khovanov Homology, Distributive Structure Homology and Applications to Knot Theory", Ph.D., pp.2017
- S. Y. Yang, "On torsion in homology of finite connected quandles", J. Knot Theory Ramifications
관련 논문AI추천
Biquandles, semi-Wirtinger number and bridge index대한수학회 · 대한수학회논문집2026 · 제41권 제1호A recursive formula for the Khovanov cohomology of Kanenobu knotsFengchun Lei, Meili Zhang대한수학회 · 대한수학회보2017 · 제54권 제1호Revisit to Connected Alexander Quandles of Small Orders via Fixed Point Free Automorphisms of Finite Abelian Groups송현종, 심효섭영남수학회 · East Asian Mathematical Journal2014 · 제30권 제3호Inner Automorphisms of an Abelian Extension of a Quandle김벼리, 배용주경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2023 · 제63권 제4호Skew brace enhancements and virtual linksMelody Chang, Sam Nelson대한수학회 · 대한수학회논문집2024 · 제39권 제1호The Intrinsic Topology on a Quandle김벼리, 김은섭, 배용주경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2017 · 제57권 제4호
이 간행물의 다른 논문 (14건)
Lightlike Hypersurfaces of an Indefinite Nearly Trans-Sasakian Manifold with an (l,m)-type Connection이철우, 이재원pp. 223-238On Alexander Polynomials of Pretzel Links배용주, 이인숙pp. 239-253Divide Knot Presentation of Knots of Berge’s Sporadic Lens Space SurgeryYuichi Yamadapp. 255-277Minkowski's Inequality for Variational Fractional IntegralsAzizollah Babakhanipp. 289-295Comparative Analysis of Spectral Theory of Second Order Difference and Differential Operators with Unbounded Odd CoefficientJoyce Mukhwana Ngala, Fredrick Oluoch Nyamwala, David Otieno Ambogopp. 297-305
