The Arc-Floer conjecture for plane curves

TL;DR

This paper proves the Arc-Floer conjecture for plane curve singularities, establishing a deep connection between contact locus cohomology and Floer cohomology of monodromy iterates.

Contribution

It provides the first proof of the conjecture in the specific case of plane curves, linking contact topology and Floer theory.

Findings

Confirmed the conjecture for plane curves

Established isomorphism between contact locus cohomology and Floer cohomology

Advances understanding of singularity invariants

Abstract

In arXiv:1911.08213 it was conjectured that the compactly supported cohomology of the $m$-th restricted contact locus of an isolated hypersurface singularity coincides, up to a shift, with the Floer cohomology of the $m$-th iterate of the monodromy of the Milnor fiber. In this paper we give an affirmative answer to this conjecture in the case of plane curves.