Canonical contact structures on some singularity links

TL;DR

This paper characterizes the canonical contact structures on certain singularity links, providing explicit diagrams for simple elliptic and cusp singularities and analyzing their properties in the Gorenstein case.

Contribution

It offers explicit Legendrian handlebody diagrams for Stein fillings of these singularities and proves the triviality of the contact structure in the Gorenstein case.

Findings

Canonical contact structures on simple elliptic and cusp singularity links are explicitly described.

Legendrian handlebody diagrams for Stein fillings are constructed.

Canonical contact structure on Gorenstein surface singularity links is trivial.

Abstract

We identify the canonical contact structure on the link of a simple elliptic or cusp singularity by drawing a Legendrian handlebody diagram of one of its Stein fillings. We also show that the canonical contact structure on the link of a numerically Gorenstein surface singularity is trivial considered as a real plane bundle.