Lecture notes on stabilization of contact open books

TL;DR

This paper discusses how contact geometric operations like surgery relate to contact open books and proves that stabilizations of contact open books produce contactomorphic manifolds, providing references for these known results.

Contribution

It offers a simple proof connecting contact surgeries to open book modifications, emphasizing the invariance of contact structures under stabilization.

Findings

Stabilizations of contact open books yield contactomorphic manifolds.

Provides a straightforward proof of contactomorphism invariance under stabilization.

Serves as a reference compilation for known contact geometric results.

Abstract

This note explains how to relate some contact geometric operations, such as surgery, to operations on an underlying contact open book. In particular, we shall give a simple proof of the fact that stabilizations of contact open books yield contactomorphic manifolds. Let us remark that the results in this note are all well known to experts. This note just aims to provide some references for these results.