Floer homology and its applications

著者

書誌事項

Floer homology and its applications

Yong-Geun Oh

（New mathematical monographs, 29 . Symplectic topology and Floer homology ; v. 2）

Cambridge University Press, 2015

  • : hardback

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注記

Includes bibliographical references (p. 429-443) and index

内容説明・目次

内容説明

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.

目次

  • 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 Weitzenboeck 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.

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