Symplectic cohomology of quasihomogeneous $cA_n$ singularities

TL;DR

This paper computes the symplectic cohomology of Milnor fibers of quasihomogeneous cAn singularities, distinguishes their contact manifold links, and supports a related conjecture.

Contribution

It provides explicit symplectic cohomology calculations for these singularities and uses them to differentiate contact structures, advancing understanding in symplectic topology.

Findings

Computed symplectic cohomology for quasihomogeneous cAn singularities

Distinguished contact manifold links of the Milnor fibers

Provided evidence supporting Evans and Lekili's conjecture

Abstract

We compute the symplectic cohomology of Milnor fibers of isolated quasihomogeneous cAn singularities . In addition, we use our computations to distinguish their links as contact manifolds and to provide further evidence to a conjecture of Evans and Lekili.