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About this book
The groundbreaking results of the near past - Donaldson's result on Lef schetz pencils on symplectic manifolds and Giroux's correspondence be tween contact structures and open book decompositions - brought a top ological flavor to global symplectic and contact geometry. This topological aspect is strengthened by the existing results of Weinstein and Eliashberg (and Gompf in dimension 4) on handle attachment in the symplectic and Stein category, and by Giroux's theory of convex surfaces, enabling us to perform surgeries on contact 3-manifolds. The main objective of these notes is to provide a self-contained introduction to the theory of surgeries one can perform on contact 3-manifolds and Stein surfaces. We will adopt a very topological point of view based on handlebody theory, in particular, on Kirby calculus for 3- and 4-dimensionalmanifolds. Surgery is a constructive method by its very nature. Applying it in an intricate way one can see what can be done. These results are nicely com plemented by the results relying on gauge theory - a theory designed to prove that certain things cannot be done. We will freely apply recent results of gauge theory without a detailed introduction to these topics; we will be content with a short introduction to some forms of Seiberg-Witten theory and some discussions regarding Heegaard Floer theory in two Appendices.
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Table of contents (15 chapters)
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Front Matter
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Back Matter
Reviews
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)
Authors and Affiliations
Bibliographic Information
Book Title: Surgery on Contact 3-Manifolds and Stein Surfaces
Authors: Burak Ozbagci, András I. Stipsicz
Series Title: Bolyai Society Mathematical Studies
DOI: https://doi.org/10.1007/978-3-662-10167-4
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2004
Hardcover ISBN: 978-3-540-22944-5Published: 29 November 2004
Softcover ISBN: 978-3-642-06184-4Published: 06 December 2010
eBook ISBN: 978-3-662-10167-4Published: 09 March 2013
Series ISSN: 1217-4696
Series E-ISSN: 2947-9460
Edition Number: 1
Number of Pages: II, 282
Additional Information: Jointly published with Janos Bolyai Mathematical Society
Topics: Geometry, Combinatorics, Topology