Matrices and Finite Biquandles
Geometric Topology
2007-05-23 v4
Abstract
We describe a way of representing finite biquandles with n elements as 2n x 2n block matrices. Any finite biquandle defines an invariant of virtual knots through counting homomorphisms. The counting invariants of non-quandle biquandles can reveal information not present in the knot quandle, such as the non-triviality of the virtual trefoil and various Kishino knots. We also exhibit a virtual knot which is distinguished from its obverse and its reverse by a finite biquandle counting invariant. We classify biquandles of order 2, 3 and 4 and provide a URL for our Maple programs for computing with finite biquandles.
Keywords
Cite
@article{arxiv.math/0601145,
title = {Matrices and Finite Biquandles},
author = {Sam Nelson and John Vo},
journal= {arXiv preprint arXiv:math/0601145},
year = {2007}
}
Comments
20 pages. Version 4: changes made as suggested by the referee. To appear in Homology, Homotopy and Applications