Quotient Quandles and the Fundamental Latin Alexander Quandle

Sam Nelson; Sherilyn Tamagawa

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arXiv · 1404.6008

Quotient Quandles and the Fundamental Latin Alexander Quandle

Sam Nelson·Sherilyn Tamagawa

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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 Gröbner 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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BibTeX RIS

Sam Nelson, Sherilyn Tamagawa. 2014-04-24. Quotient Quandles and the Fundamental Latin Alexander Quandle. https://arxiv.org/abs/1404.6008

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