Vassiliev Invariants from Parity Mappings
H. A. Dye
TL;DR
This paper introduces a new method for constructing Vassiliev invariants of virtual knots using parity mappings from Gauss diagram chords to integers, expanding the toolkit for knot invariants.
Contribution
It defines parity mappings and uses them to generate families of invariants, including degree n Vassiliev invariants, for virtual knots.
Findings
Constructed new invariants from parity mappings
Established a connection between parity and Vassiliev invariants
Provided a framework for analyzing virtual knots
Abstract
Parity mappings from the chords of a Gauss diagram to the integers is defined. The parity of the chords is used to construct families of invariants of Gauss diagrams and virtual knots. One family consists of degree Vassiliev invariants.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology