Surgery on Contact 3-Manifolds and Stein Surfaces

Surgery is the most effective way of constructing manifolds. This isespecially true in dimensions 3 and 4, where Kirby calculus provides amethod for manipulating surgery diagrams. The groundbreaking resultsof Donaldson (on Lefschetz fibrations) and Giroux (on open bookdecompositions) now allow one to incorporate analyticstructures into these diagrams: symplectic or Stein structuresin the 4-dimensional case, contact structures in the 3-dimensionalsituation. This volume gives an introduction to thesurgery techniques adapted to these additional structures.The necessary topological background on Lefschetz fibrations and openbook decompositions is developed in the book. Also included arerapid introductions to the basics and applications ofSeiberg--Witten and Heegaard Floer theories.This book is about an investigation of recent developments in the field of sympletic and contact structures on four- and three-dimensional manifolds from a topologist s point of view. In it, two main issues are addressed: what kind of sympletic and contact structures we can construct via surgery theory and what kind of sympletic and contact structures are not allowed via gauge theory and the newly invented Heegaard-Floer theory.