Symplectic Topology and Floer Homology: Volume 2, Floer Homology and its Applications

The second part of a two-volume set offering a systematic explanation of symplectic topology. This volume provides a comprehensive introduction to Hamiltonian and Lagrangian Floer theory.

Yong-Geun Oh (Author)

9781107109674, Cambridge University Press

Hardback, published 27 August 2015

472 pages, 10 b/w illus. 50 exercises
23 x 15.2 x 1.5 cm, 0.5 kg

'This volume completes a comprehensive introduction to symplectic topology and Floer theory.' Hansjorg Geiges, Mathematical Reviews

Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory, including many examples of their applications to various problems in symplectic topology. The first volume covered the basic materials of Hamiltonian dynamics and symplectic geometry and the analytic foundations of Gromov's pseudoholomorphic curve theory. Symplectic Topology and Floer Homology is a comprehensive resource suitable for experts and newcomers alike.

Preface
Part III. Lagrangian Intersection Floer Homology: 12. Floer homology on cotangent bundles
13. Off-shell framework of Floer complex with bubbles
14. On-shell analysis of Floer moduli spaces
15. Off-shell analysis of the Floer moduli space
16. Floer homology of monotone Lagrangian submanifolds
17. Applications to symplectic topology
Part IV. Hamiltonian Fixed Point Floer Homology: 18. Action functional and Conley–Zehnder index
19. Hamiltonian Floer homology
20. Pants product and quantum cohomology
21. Spectral invariants: construction
22. Spectral invariants: applications
Appendix A. The Weitzenböck formula for vector valued forms
Appendix B. Three-interval method of exponential estimates
Appendix C. Maslov index, Conley–Zehnder index and index formula
References
Index.

Subject Areas: Topology [PBP], Geometry [PBM]