Surgery on Contact 3-Manifolds and Stein Surfaces (Bolyai Society Mathematical Studies, 13) 2004th Edition by Burak Ozbagci (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review From the reviews:”This book introduces the reader to modern trends in low-dimensional contact and symplectic geometry. … They also touch on and hint at many other interesting topics. This book is a highly recommended introduction to this exciting circle of ideas.” (John B. Etnyre, Mathematical Reviews, Issue 2005 k) From the Back Cover 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.

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