On symplectic caps

TL;DR

This paper explicitly describes symplectic caps for certain contact 3-manifolds arising from rational surface singularities and introduces a new obstruction to their rational homology disk smoothings.

Contribution

It provides explicit descriptions of symplectic caps for contact 3-manifolds linked to rational surface singularities and introduces a novel obstruction for smoothings.

Findings

Explicit descriptions of symplectic caps for specific contact 3-manifolds.

A new obstruction criterion for rational homology disk smoothings.

Application to the study of rational surface singularities.

Abstract

An important class of contact 3--manifolds are those that arise as links of rational surface singularities with reduced fundamental cycle. We explicitly describe symplectic caps (concave fillings) of such contact 3--manifolds. As an application, we present a new obstruction for such singularities to admit rational homology disk smoothings.