University of Massachusetts Amherst
	Department of Mathematics and Statistics
	Geometry and Topology Seminar

Abstract: A famous theorem of Giroux establishes a correspondence between open book decompositions and contact structures on 3-manifolds; a contact structure can arise on the boundary of Stein manifods iff it has an open books with positive monodromy (in this case a Stein fillings can be constructed as a Lefschetz fibration). Although in general one needs to study all stabilizations of open books to understand all Stein fillings, in the genus zero case it suffices to analyze the monofromy of a single open book (due to a recent result of Wendl). I will review the basics on open books, contact structures, and Stein fillings in some detail, and then explain how factorizations of monodromy lead to classification of fillings of certain lens spaces, and to some non-fillability results. (Joint with J. Van Horn-Morris.)