Virtual index cocycles and invariants of virtual links
Igor Nikonov
TL;DR
This paper introduces the virtual index cocycle, a new mathematical tool for analyzing virtual links, which helps unify and reformulate existing invariants in virtual knot theory.
Contribution
It presents the virtual index cocycle as a novel approach to understanding virtual link invariants, providing a unifying framework.
Findings
Reformulation of known virtual link invariants
Unification of different invariants using the cocycle
Potential new insights into virtual link classification
Abstract
Virtual index cocycle is the 1-cochain that counts virtual crossings in the arcs of a virtual link diagram. We show how this cocycle can be used to reformulate and unify some known invariants of virtual links.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Advanced Combinatorial Mathematics · Data Visualization and Analytics