Link invariants from finite Coxeter racks

Preprint English OPEN
Nelson, Sam ; Wieghard, Ryan (2008)
  • Subject: 57M2, 57M27, 17D99 | Mathematics - Quantum Algebra | Mathematics - Geometric Topology
    arxiv: Mathematics::Geometric Topology | Mathematics::Quantum Algebra | Computer Science::Robotics | Mathematics::Category Theory

We study Coxeter racks over $\mathbb{Z}_n$ and the knot and link invariants they define. We exploit the module structure of these racks to enhance the rack counting invariants and give examples showing that these enhanced invariants are stronger than the unenhanced rack counting invariants.
  • References (9)

    [1] E. Brieskorn, Automorphic sets and braids and singularities. Contemp. Math. 78 (1988) 45-115.

    [2] D. Joyce. A classifying invariant of knots, the knot quandle. J. Pure Appl. Algebra 23 (1982) 37-65.

    [3] R. Fenn and C. Rourke. Racks and links in codimension two. J. Knot Theory Rami cations 1 (1992), 343-406.

    [4] S. V. Matveev. Distributive groupoids in knot theory. Math. USSR, Sb. 47 (1984) 73-83.

    [5] E.A. Navas and S. Nelson. On symplectic quandles. To appear in Osaka J. Math., arXiv:math/0703727

    [6] S. Nelson. A polynomial invariant of nite racks. J. Alg. Appl. 7 (2008) 263-273.

    [7] S. Nelson. Link invariants from nite racks. arXiv:0808.0029

    [8] S. Nelson and J.L. Rische. On bilinear biquandles. Colloq. Math. 112 (2008) 279-289.

    [9] M. Takasaki. Abstraction of symmetric transformation (in Japanese). Tohoku Math J. 49 (1943) 145-207. Department of Mathematics, Claremont McKenna College, 850 Colubmia Ave., Claremont, CA 91711 Email address: Department of Mathematics, Pomona College, 610 N. College Ave., Claremont, CA 91711 Email address:

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