Surgery is the most effective way of constructing manifolds. This is especially true in dimensions 3 and 4, where Kirby calculus provides a method for manipulating surgery diagrams. The groundbreaking results of Donaldson (on Lefschetz fibrations) and Giroux (on open book decompositions) now allow one to incorporate analytic structures into these diagrams: symplectic or Stein structures in the 4-dimensional case, contact structures in the 3-dimensional situation. This volume gives an introduction to the surgery techniques adapted to these additional structures. The necessary topological background on Lefschetz fibrations and open book decompositions is developed in the book. Also included are rapid introductions to the basics and applications of Seiberg--Witten and Heegaard Floer theories.
CONTENT
1. Introduction -- 2. Topological Surgeries -- 3. Symplectic 4-Manifolds -- 4. Contact 3-Manifolds -- 5. Convex Surfaces in Contact 3-Manifolds -- 6. Spinc Structures on 3- and 4-Manifolds -- 7. Symplectic Surgery -- 8. Stein Manifolds -- 9. Open Books and Contact Structures -- 10. Lefschetz Fibrations on 4-Manifolds -- 11. Contact Dehn Surgery -- 12. Fillings of Contact 3-Manifolds -- 13. Appendix: Seibergโ{128}{148}Witten Invariants -- 14. Appendix: Heegaard Floer Theory -- 15. Appendix: Mapping Class Groups
