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

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.

arXiv comment18 pages, 16 figures, v5: contains new examples and a section on gluing contact 3-manifolds with convex boundary