Virtual Yang-Baxter cocycle invariants
Jose Ceniceros, Sam Nelson
TL;DR
This paper introduces an extension of Yang-Baxter cocycle invariants for virtual knots, combining cohomology theories to enhance detection of virtual knot non-classicality beyond classical invariants.
Contribution
It develops a novel method that augments classical Yang-Baxter cocycle invariants with virtual biquandle cohomology, enabling better detection of virtual knot properties.
Findings
Invariants coincide with classical ones for classical knots
New invariants detect non-classical virtual knots
Method provides additional information about virtual links
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models