Virtual Yang-Baxter cocycle invariants

Details Virtual Yang-Baxter cocycle invariants Virtual Yang-Baxter cocycle invariants

2007-08-31

arxiv.org/abs/0708.4254v2

Mathematics

Geometric Topology

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

Scientific paper

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.

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