Topology Atlas | Conferences

Knots in Washington XLI
December 4-6, 2015
George Washington University
Washington, DC, USA

Organizers
Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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Parity Biquandle Invariants of Virtual Knots
by
Leo Selker
Pomona College
Coauthors: Sam Nelson (Claremont McKenna College), Aaron Kaestner (North Park University)

Given a biquandle X, we have a biquandle counting invariant and a biquandle cocycle invariant. In order to capture more structure of virtual knots, we use parity biquandles to construct the parity biquandle counting invariant. We also use parity biquandles to add additional structure to the cocycle invariant. We use a parity biquandle cocycle together with a compatible function to construct the parity-enhanced biquandle cocycle polynomial, which has the biquandle cocycle invariant as a special case. We consider some examples where these enhancements are nontrivial.

Date received: September 29, 2015

Copyright © 2015 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cblw-04.