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.
Partial open book decomposition, contact three-manifold with convex boundary, sutured manifold, sutured Floer homology, EH-contact class.
ETGÜ, TOLGA and ÖZBAĞCI, BURAK
"Partial open book decompositions and the contact class in sutured floer homology,"
Turkish Journal of Mathematics: Vol. 33:
3, Article 10.
Available at: https://journals.tubitak.gov.tr/math/vol33/iss3/10