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.
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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