Ken Baker

Department of Mathematics,
University of Miami,
Coral Gables, FL 33124, USA.

Title: Open Books and Contact Structures on 3-Manifolds I: Contact Structures from Open Books

Abstract: While Thurston-Winkelnkemper exhibited a way of inducing a contact structure from an open book, Giroux clarified this with the notion of an open book supporting a contact structure and then showing any two contact structures supported by an open book are isotopic. In this first talk we will introduce the basic concepts involved in contact structures, open books, and their relationships.

Title: Open Books and Contact Structures on 3-Manifolds II: Contact Cell Decompositions

Abstract: In this second talk we aim to show that every co-orientable contact structure on a closed compact 3-manifold is supported by an open book. To do so, we investigate Giroux's theory of contact cell decompositions and their relationships to open books. From there we will give the outline of Giroux's Correspondence and discuss some of its consequences.

Title: Open Books and Contact Structures on 3-Manifolds III: Dehn Surgery and Open Books

Abstract: Through Heegaard Floer homology, it is now known that any knot admitting a Dehn surgery from $S^3$ to certain exceptional manifolds ($L$-spaces) must be fibered and hence defines an open book. The surgery dual of such a knot has the same exterior and thus also fibers, but it typically won't induce the usual sort of open book. In this final talk we'll discuss Dehn surgery on bindings of open books and develop rational open books and their integral resolutions with an eye towards questions in Dehn surgery.