Biquandle Module Quiver Representations

TL;DR

This paper introduces a new family of invariants for knots and links using biquandle modules and quiver representations, leading to novel polynomial invariants that distinguish various knot types.

Contribution

It develops an infinite family of quiver representation-valued invariants based on biquandle modules, extending knot invariants to a broader class of knots and links.

Findings

Defined new quiver invariants for classical, virtual, and surface-knots.

Constructed two-variable polynomial invariants from these quivers.

Demonstrated the invariants' effectiveness in distinguishing knot types.

Abstract

We introduce an infinite family of quiver representation-valued invariants of classical, virtual and surface-knots and links associated to a choice of finite biquandle, commutative unital ring, biquandle module and set of biquandle endomorphisms. As an application, we use this quiver to define a new infinite family of two-variable polynomial invariants.