Surgeries on the trefoil and symplectic fillings

TL;DR

This paper investigates the Stein fillability of contact structures on manifolds derived from surgeries on the right-handed trefoil, revealing complex patterns and contributing to the understanding of contact topology.

Contribution

It determines which contact structures from surgeries on the trefoil are Stein fillable, highlighting the complexity and lack of clear patterns in fillability.

Findings

Certain surgeries produce Stein fillable contact structures

Many contact structures from trefoil surgeries are not Stein fillable

The results suggest no simple pattern governs fillability

Abstract

In this note we will determine which contact structures on manifolds obtained by certain surgeries on the right handed trefoil are Stein fillable and which are not. This continues a long line of research and shows that there seems to be few underlying patterns to when a contact structure is Stein fillable or not.