Categorification of Biquandle Arrow Weight Invariants via Quivers

TL;DR

This paper develops a categorification of biquandle arrow weight invariants for knots, creating new polynomial invariants through biquandle coloring quivers, enhancing the understanding of virtual and classical knot invariants.

Contribution

It introduces a novel categorification approach using biquandle coloring quivers to generate infinite families of polynomial knot invariants.

Findings

New polynomial invariants for knots derived from categorification.

Infinite families of invariants enhance previous biquandle arrow weight invariants.

Application to both virtual and classical knots.

Abstract

Introduced in arXiv:2211.12606, biquandle arrow weight invariants are enhancements of the biquandle counting invariant for oriented virtual and classical knots defined from biquandle-colored Gauss diagrams using a tensor over an abelian group satisfying certain properties. In this paper we categorify the biquandle arrow weight polynomial invariant using biquandle coloring quivers, obtaining new infinite families of polynomial invariants of oriented virtual and classical knots.