Morsifications and mutations

TL;DR

This paper explores the relationship between the topology of plane curve singularities and the mutation equivalence of quivers derived from their morsifications, linking algebraic and topological aspects.

Contribution

It introduces a novel connection between singularity topology and cluster algebra mutations through the study of morsifications.

Findings

Established a correspondence between singularity topology and quiver mutations.

Identified conditions under which quivers are mutation equivalent.

Provided new insights into the algebraic structure of singularities.

Abstract

We describe and investigate a connection between the topology of isolated singularities of plane curves and the mutation equivalence, in the sense of cluster algebra theory, of the quivers associated with their morsifications.