Contact Invariant in Sutured Floer Homology

Gordana Matic, University of Georgia at Athens

An open book decomposition compatible with a contact structure on a
closed contact manifold was used by Ozsvath and Szabo to define the
contact invariant in Heegard Floer homology.  We will describe how to
use a "partial open book decomposition" to define an invariant of a
contact manifold with convex boundary as an element in Juhasz's
sutured Floer homology. We will describe the natural map induced by
embedding a sutured manifold into a larger manifold, some gluing
theorems and some consequences. This is joint work with Ko Honda and
Will Kazez.