Lectures on open book decompositions and contact structures

TL;DR

This paper provides an overview of the Giroux correspondence linking open book decompositions and contact structures on three-manifolds, including its proof sketch and applications, within the context of low-dimensional topology.

Contribution

It offers a detailed sketch of the proof of Giroux correspondence and explores its various applications in contact topology.

Findings

Giroux correspondence established between open books and contact structures

Proof sketch of Giroux correspondence provided

Applications in low-dimensional topology discussed

Abstract

These are lecture notes from the Clay Mathematics Institute summer school ``Floer Homology, Gauge Theory, and Low Dimensional Topology'' Alfred Renyi Institute; www.claymath.org/programs/summer_school/2004/. The main goal of these notes is to sketch a proof of Giroux correspondence between open book decompositions of three manifolds and contact structures, and then discuss various applications of this correspondence.