Persistent Homology of Biquandle Coloring Quivers

TL;DR

This paper develops a new homology theory for biquandle coloring quivers, leading to persistent invariants of links that extend classical topological invariants using quiver filtrations.

Contribution

It introduces a novel homology theory for quivers derived from biquandle colorings and constructs persistent invariants of links based on quiver filtrations.

Findings

New homology theory for biquandle coloring quivers

Persistent link invariants from quiver filtrations

Extension of directed clique complex concepts

Abstract

In this paper, we extend the notion of directed clique complex to quivers and introduce an associated homology theory. By applying this construction to biquandle coloring quivers, we obtain new invariants of links. We then introduce a quiver filtration-valued invariant of links induced by filtrations of biquandle endomorphism sets. We construct persistent homological invariants of links by applying persistence techniques to these quiver filtrations through the introduced homology theory.