Biquandle Bracket Quivers

TL;DR

This paper introduces biquandle bracket quivers, a new categorification framework that unites biquandle coloring quivers and skein invariants, leading to infinite categorifications of classical knot invariants like the Jones polynomial.

Contribution

It unites biquandle coloring quivers with skein invariants to create biquandle bracket quivers, offering new categorifications of classical knot invariants.

Findings

Provides a new categorification framework for biquandle brackets.

Creates an infinite family of categorifications of the Jones polynomial.

Unifies existing invariants into a broader categorification approach.

Abstract

Biquandle brackets define invariants of classical and virtual knots and links using skein invariants of biquandle-colored knots and links. Biquandle coloring quivers categorify the biquandle counting invariant in the sense of defining quiver-valued enhancements which decategorify to the counting invariant. In this paper we unite the two ideas to define biquandle bracket quivers, providing new categorifications of biquandle brackets. In particular, our construction provides an infinite family of categorifications of the Jones polynomial and other classical skein invariants.