Virtual Yang-Baxter cocycle invariants

Abstract

We extend the Yang-Baxter cocycle invariants for virtual knots by augmenting Yang-Baxter 2-cocycles with cocycles from a cohomology theory associated to a virtual biquandle structure. These invariants coincide with the classical Yang-Baxter cocycle invariants for classical knots but provide extra information about virtual knots and links. In particular, they provide a method for detecting non-classicality of virtual knots and links.

17 pages, many pictures. To appear in Trans. Amer. Math. Soc. Version 2 includes minor typo corrections

References in corpus (2)

• Homology Theory for the Set-Theoretic Yang-Baxter Equation and Knot Invariants from Generalizations of Quandles
• Biquandles for Virtual Knots