Lower bounds on virtual crossing number and minimal surface genus
Kumud Bhandari, H. A. Dye, and Louis H. Kauffman
TL;DR
This paper establishes lower bounds for the virtual crossing number and minimal surface genus of virtual knots using the arrow polynomial, providing insights into their complexity and structure.
Contribution
It introduces a method to derive lower bounds on virtual crossing number and surface genus from the arrow polynomial, advancing understanding of virtual knot invariants.
Findings
Lower bounds on virtual crossing number derived from arrow polynomial.
Lower bounds on minimal surface genus established.
Application to specific virtual knot examples.
Abstract
We compute lower bounds on the virtual crossing number and minimal surface genus of virtual knot diagrams from the arrow polynomial. In particular, we focus on several interesting examples.
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Taxonomy
TopicsGeometric and Algebraic Topology · Computational Geometry and Mesh Generation · Advanced Combinatorial Mathematics