Table of contents for Surgery on contact 3-manifolds and stein surfaces / Burak Ozbagci, András I. Stipsicz.


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C O NTENTS  ...................................... ....................  3
PREFACE   ............................ .....................................  7
1. INTRODUCTION    ........................................... .......  11
1.1. Why symplectic and contact? ............................... 11
1.2. Results concerning Stein surfaces ........................... 13
1.3. Some contact results ...................................... . 21
2. TOPOLOGICAL    SURGERIES  .........................................  25
2.1. Surgeries and handlebodies .................................. 25
2.2. Dehn  surgery  ................................................  31
2.3. Kirby  calculus  ...............................................  38
3. SYMPLECTIC 4-MANIFOLDS ........................................ 49
3.1. Generalities about symplectic manifolds ...................   49
3.2. Moser's method and neighborhood theorems ...............      55
3.3. Appendix: The complex classification scheme for symplectic
4-m anifolds  ............................................. .....  58
4. CONTACT   3-MANIFOLDS   ...........................................  63
4.1. Generalities on contact 3-manifolds ........................ 63
4.2. Legendrian knots ............................................ 72
4.3. Tight versus overtwisted structures ......................... 76
5. CONVEX SURFACES IN CONTACT 3-MANIFOLDS .................... 85
5.1. Convex surfaces and dividing sets .........................   85
5.2. Contact structures and Heegaard decompositions ............ 96
6. Spinc STRUCTURES ON 3- AND 4-MANIFOLDS ...................... 99
6.1. Generalities on spin and spinc structures .................... 99
6.2. Spin0 structures and oriented 2-plane fields .................. 102
6.3. Spine structures and almost-complex structures .............. 105
7. SYMPLECTIC SURGERY ............................................ 111
7.1. Symplectic cut-and-paste ...............  .............. 111
7.2. W einstein  handles  .......................... ................  115
7.3. Another handle attachment .................................119
8. STEIN MANIFOLDS ................................................ 121
8.1. Recollections and definitions ................ ............ 121
8.2. Handle attachment to Stein manifolds ...................... 125
8.3. Stein neighborhoods of surfaces ............................ 127
9. OPEN BOOKS AND CONTACT STRUCTURES ..................... 131
9.1. Open book decompositions of 3-manifolds .................. 131
9.2. Compatible contact structures ........................... 138
9.3. Branched covers and contact structures .................... 150
10. LEFSCHETZ FIBRATIONS ON 4-MANIFOLDS ........................ 155
10.1. Lefschetz pencils and fibrations ............................. 155
10.2. Lefschetz fibrations on Stein domains ..................... 162
10.3. Som e  applications  .......................................... 173
11. CONTACT DEHN SURGERY ....................................... 179
11.1. Contact structures on S1 x D2 .......................... 179
11.2. Contact Dehn surgery ....................  .............. 185
11.3. Invariants of contact structures given by surgery diagrams .. 191
12. FILLINGS OF CONTACT 3-MANIFOLDS ............................ 201
12.1. Fillings  ................................. .... ............. . 201
12.2. Nonfillable contact 3-manifolds .......................... 206
12.3. Topology of Stein fillings ................................ 215
13. APPENDIX: SEIBERG-WITTEN INVARIANTS ...................... 223
13.1. Seiberg-Witten invariants of closed 4-manifolds ........... 223
13.2. Seiberg-Witten invariants of 4-manifolds with contact boun-
dary  ......................................................... 229
13.3. The adjunction inequality ................................. 231
14. APPENDIX: HEEGAARD FLOER THEORY .......................... 235
14.1. Topological preliminaries ................................... 235
14.2. Heegaard Floer theory for 3- and 4-manifolds ............. 239
14.3. Surgery  triangles  ................  ........................ 244
14.4. Contact Ozsvdth-Szab6 invariants ......................... 249
15. APPENDIX: MAPPING CLASS GROUPS ............................ 255
15.1. Short introduction ............. ......................   . 255
15.2. Mapping class groups and geometric structures ............. 263
15.3. Som e  proofs  ................. ........ ..................... 265
BIBLIOGRAPHY .................................................... 269
IN DEX  ........................................ ......................  279



Library of Congress subject headings for this publication: Surgery (Topology)Three-manifolds (Topology)Surfaces