Virtual Crossing Number and the Arrow Polynomial
H. A. Dye, Louis H. Kauffman
TL;DR
This paper introduces a new polynomial invariant for virtual knots and links, which helps in estimating the minimal number of virtual crossings and the surface genus needed for their representation.
Contribution
The paper presents a novel polynomial invariant specifically designed for virtual knots and links, providing a new tool for analyzing their complexity.
Findings
Provides a lower bound on virtual crossing number
Establishes a lower bound on minimal surface genus
Introduces a new polynomial invariant for virtual knots
Abstract
We introduce a new polynomial invariant of virtual knots and links and use this invariant to compute a lower bound on the virtual crossing number and the minimal surface genus.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Computational Geometry and Mesh Generation