An open book decomposition compatible with rational contact surgery

TL;DR

This paper develops a method to construct open book decompositions compatible with contact structures resulting from rational contact surgeries on Legendrian links, and explores their implications for overtwisted structures.

Contribution

It introduces a new construction of open book decompositions compatible with rational contact surgeries on Legendrian links.

Findings

Some rational contact surgeries induce overtwisted contact structures.

The construction applies to Legendrian links in standard contact 3-sphere.

Provides tools for analyzing contact structures via open book decompositions.

Abstract

We construct an open book decomposition compatible with a contact structure given by a rational contact surgery on a Legendrian link in the standard contact $S^3$. As an application we show that some rational contact surgeries on certain Legendrian knots induce overtwisted contact structures.