Matrices and Finite Biquandles

Details Matrices and Finite Biquandles Matrices and Finite Biquandles

2006-01-07

arxiv.org/abs/math/0601145v4

Homology, Homotopy and Applications 8 (2006) 51-73.

Mathematics

Geometric Topology

20 pages. Version 4: changes made as suggested by the referee. To appear in Homology, Homotopy and Applications

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Matrices and Finite Biquandles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Matrices and Finite Biquandles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Matrices and Finite Biquandles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-65798