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Mathematics - Geometry & Topology | Surgery on Contact 3-Manifolds and Stein Surfaces

Surgery on Contact 3-Manifolds and Stein Surfaces

Ozbagci, Burak, Stipsicz, András

Jointly published with Janos Bolyai Mathematical Society

2004, II, 282 p.

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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 Level » Research

Keywords » 3-manifolds - Contact Geometry - Contact Surgery - Stein Surfaces - Topology - mapping

Related subjects » Geometry & Topology

Table of contents 

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: Seiberg—Witten Invariants.- 14. Appendix: Heegaard Floer Theory.- 15. Appendix: Mapping Class Groups.

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