Writhe polynomial for virtual links
Mengjian Xu
TL;DR
This paper introduces a new writhe polynomial for virtual links using a weak chord index, providing invariants that help distinguish non-trivial virtual knots like the Kishino knot.
Contribution
It defines a novel writhe polynomial for virtual links and constructs invariants that improve detection of non-trivial virtual knots.
Findings
The new writhe polynomial generalizes previous invariants.
The invariants can detect non-trivial virtual knots such as the Kishino knot.
The approach enhances the ability to distinguish virtual link complexities.
Abstract
A weak chord index is constructed for self crossing points of virtual links. Then a new writhe polynomial of virtual links is defined by using . is a generalization of writhe polynomial defined in [6]. Based on , three invariants of virtual links are constructed. These invariants can be used to detect the non-trivialities of Kishino knot and flat Kishino knot.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology