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

by Yong-Geun Oh

Overview

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.

Product Details

ISBN-13:	9781107109674
Publisher:	Cambridge University Press
Publication date:	08/27/2015
Series:	New Mathematical Monographs , #29
Pages:	472
Product dimensions:	5.98(w) x 9.06(h) x 0.59(d)

About the Author

Yong-Geun Oh is Director of the IBS Center for Geometry and Physics and is Professor in the Department of Mathematics at POSTECH (Pohang University of Science and Technology) in Korea. He was also Professor in the Department of Mathematics at the University of Wisconsin, Madison. He is a member of the KMS, the AMS, the Korean National Academy of Sciences, and the inaugural class of AMS Fellows. In 2012 he received the Kyung-Ahm Prize for Science in Korea.

Table of Contents

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.

Editorial Reviews

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

From the Publisher