New York Journal of Mathematics
Volume 22 (2016) 251-263


Sam Nelson and Sherilyn Tamagawa

Quotient quandles and the fundamental Latin Alexander quandle

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Published: March 9, 2016
Keywords: Quandles, Alexander quandles, Latin quandles, knot invariants, Gröbner bases
Subject: 57M27, 57M25

Defined in Joyce, 1982, and Matveev, 1984, the fundamental quandle is a complete invariant of oriented classical knots up to ambient homeomorphism. We consider invariants of knots defined from quotients of the fundamental quandle. In particular, we introduce a generalization of the Alexander quandle of a knot known as the fundamental Latin Alexander quandle 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.


The first author was partially supported by Simons Foundation collaboration grant 316709

Author information

Sam Nelson:
Department of Mathematics, Claremont McKenna College, 850 Columbia Ave., Claremont, CA 91711

Sherilyn Tamagawa:
Department of Mathematics, South Hall, Room 6607, University of California, Santa Barbara, CA 93106-3080