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arXiv · 1507.05583

Parity Biquandle Invariants of Virtual Knots

Aaron Kaestner·Sam Nelson·Leo Selker
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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.

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BibTeXRIS

Aaron Kaestner, Sam Nelson, Leo Selker. 2015-07-20. Parity Biquandle Invariants of Virtual Knots. https://arxiv.org/abs/1507.05583

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