Bowling ball representation of virtual string links
Zhiyun Cheng
TL;DR
This paper introduces a probabilistic approach to virtual string links, utilizing virtual flat biquandles and cocycle invariants to distinguish them from classical links, advancing algebraic understanding in knot theory.
Contribution
It proposes the virtual flat biquandle and cocycle invariants as new tools for analyzing virtual string links, offering a novel algebraic framework.
Findings
Probabilistic interpretation distinguishes some virtual from classical links
Introduction of virtual flat biquandle as an algebraic structure
Discussion of cocycle invariants related to virtual flat biquandles
Abstract
In this paper we investigate the virtual string links via a probabilistic interpretation. This representation can be used to distinguish some virtual string links from classical string links. In order to study the algebraic structure behind this probabilistic interpretation we introduce the notion of virtual flat biquandle. The cocycle invariants associated with virtual flat biquandle is discussed.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics