Partial open book decompositions and the contact class in sutured Floer homology

TL;DR

This paper presents a combinatorial method to compute the contact class in sutured Floer homology for manifolds derived from partial open book decompositions, enabling new insights into contact structures.

Contribution

It introduces a combinatorial approach to calculate the EH-class in sutured Floer homology for partial open book decompositions, linking contact structures to handlebody gluings.

Findings

Combinatorial calculation of the EH-class is possible for compatible contact structures.

Every contact 3-manifold can be constructed from tight handlebodies with nontrivial EH-classes.

The method applies to both closed and boundary-possessing contact 3-manifolds.

Abstract

We demonstrate how to combinatorially calculate the EH-class of a compatible contact structure in the sutured Floer homology group of a balanced sutured three manifold which is associated to an abstract partial open book decomposition. As an application we show that every contact three manifold (closed or with convex boundary) can be obtained by gluing tight contact handlebodies whose EH-classes are nontrivial.