Foundations of topological racks and quandles

Article, Preprint English OPEN
Mohamed Moutuou, El-Kaioum; Elhamdadi, Mohamed;
  • Related identifiers: doi: 10.1142/S0218216516400022
  • Subject: Mathematics - Algebraic Topology | Mathematics - Rings and Algebras | Mathematics - Quantum Algebra | 57M25, 20E22, 22E41 | Mathematics - Geometric Topology
    arxiv: Mathematics::Geometric Topology | Mathematics::Quantum Algebra | Computer Science::Robotics | Mathematics::Category Theory

We give a foundational account on topological racks and quandles. Specifically, we define the notions of ideals, kernels, units, and inner automorphism group in the context of topological racks. Further, we investigate topological rack modules and principal rack bundles... View more
  • References (19)
    19 references, page 1 of 2

    [1] N. Andruskiewitsch and M. Graña, From racks to pointed Hopf algebras, Adv. Math. 178 (2003), no. 2, 177-243, doi: 10.1016/S0001-8708(02)00071-3. MR1994219 (2004i:16046)

    [2] J. S. Carter, A. S. Crans, M. Elhamdadi, and M. Saito, Cohomology of categorical selfdistributivity, J. Homotopy Relat. Struct. 3 (2008), no. 1, 13-63. MR2395367 (2010b:16069)

    [3] J. S. Carter, M. Elhamdadi, M. Graña, and M. Saito, Cocycle knot invariants from quandle modules and generalized quandle homology, Osaka J. Math. 42 (2005), no. 3, 499-541. MR2166720 (2006d:57017)

    [4] J. S. Carter, M. Elhamdadi, and M. Saito, Twisted quandle homology theory and cocycle knot invariants, Algebr. Geom. Topol. 2 (2002), 95-135 (electronic), doi: 10.2140/agt.2002.2.95. MR1885217 (2003a:57019)

    [5] J. S. Carter, D. Jelsovsky, S. Kamada, L. Langford, and M. Saito, Quandle cohomology and state-sum invariants of knotted curves and surfaces, Trans. Amer. Math. Soc. 355 (2003), no. 10, 3947-3989, doi: 10.1090/S0002-9947-03-03046-0. MR1990571 (2005b:57048)

    [6] W. E. Clark, M. Elhamdadi, M. Saito, and T. Yeatman, Quandle colorings of knots ematical Library, vol. 74, American Mathematical Society, Providence, RI, 2015, (to appear).

    [9] P. Etingof and M. Graña, On rack cohomology, J. Pure Appl. Algebra 177 (2003), no. 1, 49-59, doi: 10.1016/S0022-4049(02)00159-7. MR1948837 (2004e:55006)

    [10] N. Jackson, Extensions of racks and quandles, Homology Homotopy Appl. 7 (2005), no. 1, 151-167. MR2155522 (2006f:18006)

    [11] M. Jacobsson and R. Rubinsztein, Symplectic Topology of SU(2)-Representation Varieties and Link Homology, I: Symplectic Braid Action and the First Chern Class, arXiv:0806.2902v3, 2009.

    [12] D. Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982), no. 1, 37-65, doi: 10.1016/0022-4049(82)90077-9. MR638121 (83m:57007)

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