Surgery on Contact 3-Manifolds and Stein Surfaces - (Bolyai Society Mathematical Studies) by Burak Ozbagci & Andras Stipsicz (Hardcover)
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<p/><br></br><p><b> Book Synopsis </b></p></br></br><p>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.</p><p/><br></br><p><b> From the Back Cover </b></p></br></br><p>Surgery is the most effective way of constructing manifolds. This is<br>especially true in dimensions 3 and 4, where Kirby calculus provides a<br>method for manipulating surgery diagrams. The groundbreaking results<br>of Donaldson (on Lefschetz fibrations) and Giroux (on open book<br>decompositions) now allow one to incorporate analytic<br>structures into these diagrams: symplectic or Stein structures<br>in the 4-dimensional case, contact structures in the 3-dimensional<br>situation. This volume gives an introduction to the<br>surgery techniques adapted to these additional structures.<br>The necessary topological background on Lefschetz fibrations and open<br>book decompositions is developed in the book. Also included are<br>rapid introductions to the basics and applications of<br>Seiberg--Witten and Heegaard Floer theories.</p> <p> </p><p/><br></br><p><b> Review Quotes </b></p></br></br><br><p>From the reviews: </p> <p></p> <p>"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)</p><br>
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