English

Quotient Quandles and the Fundamental Latin Alexander Quandle

Geometric Topology 2014-04-25 v1 Quantum Algebra

Abstract

Defined by Joyce and Matveev, the fundamental quandle is a complete invariant of oriented classical knots. We consider invariants of knots defined from quotients of the fundamental quandle. In particular, we introduce the fundamental Latin Alexander quandle of a knot and consider its Gr\"obner basis-valued invariants, which generalize the Alexander polynomial. We show via example that the invariant is not determined by the generalized Alexander polynomial for virtual knots.

Keywords

Cite

@article{arxiv.1404.6008,
  title  = {Quotient Quandles and the Fundamental Latin Alexander Quandle},
  author = {Sam Nelson and Sherilyn Tamagawa},
  journal= {arXiv preprint arXiv:1404.6008},
  year   = {2014}
}

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11 pages