Title: Tightness and open book decompositions

Abstract: A well known result of Giroux tells us that isotopy classes of 
contact structures on a closed three manifold are in one to one 
correspondence with stabilization classes of open book decompositions of 
the manifold. We will introduce a stabilization-invariant property of open 
books which corresponds to tightness of the corresponding contact 
structure. We will mention applications to the classification of contact 
3-folds, and also to the question of whether tightness is preserved under 
Legendrian surgery.