Parity Biquandle Invariants of Virtual Knots
Geometric Topology
2016-06-16 v2 Quantum Algebra
Abstract
We define counting and cocycle enhancement invariants of virtual knots using parity biquandles. These invariants are determined by pairs consisting of a biquandle 2-cocycle \phi^0 and a map \phi^1 with certain compatibility conditions leading to one-variable or two-variable polynomial invariants of virtual knots. We provide examples to show that the parity cocycle invariants can distinguish virtual knots which are not distinguished by the corresponding non-parity invariants.
Keywords
Cite
@article{arxiv.1507.05583,
title = {Parity Biquandle Invariants of Virtual Knots},
author = {Aaron Kaestner and Sam Nelson and Leo Selker},
journal= {arXiv preprint arXiv:1507.05583},
year = {2016}
}
Comments
12 pages; v2 includes changes suggested by referee