Psyquandle Coloring Quivers

TL;DR

This paper introduces a novel quiver-based enhancement of the psyquandle coloring invariant, extending it to singular knots and pseudoknots, and deriving new polynomial invariants for classical and virtual knots.

Contribution

It develops a new quiver-based framework for psyquandle invariants, broadening their applicability to singular and pseudoknots, and introduces in-degree polynomial invariants.

Findings

Extended invariants to singular knots and pseudoknots

Derived biquandle coloring quivers for classical and virtual knots

Produced new polynomial invariants for various knot types

Abstract

We enhance the psyquandle counting invariant for singular knots and pseudoknots using quivers analogously to quandle coloring quivers. This enables us to extend the in-degree polynomial invariants from quandle coloring quiver theory to the case of singular knots and pseudoknots. As a side effect we obtain biquandle coloring quivers and in-degree polynomial invariants for classical and virtual knots and links.