Surgery on Contact 3-Manifolds and Stein Surfaces

1. Front Matter

   Pages i-9

   PDF

2. Introduction

   • Burak Ozbagci, András I. Stipsicz

   Pages 11-24

3. Topological Surgeries

   • Burak Ozbagci, András I. Stipsicz

   Pages 25-48

4. Symplectic 4-Manifolds

   • Burak Ozbagci, András I. Stipsicz

   Pages 49-62

5. Contact 3-Manifolds

   • Burak Ozbagci, András I. Stipsicz

   Pages 63-84

6. Convex Surfaces in Contact 3-Manifolds

   • Burak Ozbagci, András I. Stipsicz

   Pages 85-98

7. Spin^c Structures on 3- and 4-Manifolds

   • Burak Ozbagci, András I. Stipsicz

   Pages 99-109

8. Symplectic Surgery

   • Burak Ozbagci, András I. Stipsicz

   Pages 111-120

9. Stein Manifolds

   • Burak Ozbagci, András I. Stipsicz

   Pages 121-130

10. Open Books and Contact Structures

    • Burak Ozbagci, András I. Stipsicz

    Pages 131-153

11. Lefschetz Fibrations on 4-Manifolds

    • Burak Ozbagci, András I. Stipsicz

    Pages 155-178

12. Contact Dehn Surgery

    • Burak Ozbagci, András I. Stipsicz

    Pages 179-200

13. Fillings of Contact 3-Manifolds

    • Burak Ozbagci, András I. Stipsicz

    Pages 201-222

14. Appendix: Seiberg-Witten Invariants

    • Burak Ozbagci, András I. Stipsicz

    Pages 223-233

15. Appendix: Heegaard Floer Theory

    • Burak Ozbagci, András I. Stipsicz

    Pages 235-254

16. Appendix: Mapping Class Groups

    • Burak Ozbagci, András I. Stipsicz

    Pages 255-268

17. Back Matter

    Pages 269-282

    PDF

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.

• 3-manifolds
• Contact Geometry
• Contact Surgery
• Stein Surfaces
• Topology
• mapping
• combinatorics

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)

• Koc University, Istanbul, Turkey

  Burak Ozbagci

• Hungarian Academy of Sciences, Alfréd Rényi Institute of Mathematics, Budapest, Hungary

  András I. Stipsicz

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