Floer homology on symplectic manifolds.

• Other Authors: Kwong, Kwok Kun.
• Format: Others
• Language: English; Chinese
• Published: 2008
• Subjects: Symplectic manifolds; Floer homology; Morse theory
• Online Access: http://library.cuhk.edu.hk/record=b5893711; http://repository.lib.cuhk.edu.hk/en/item/cuhk-326359

Kwong, Kwok Kun. === Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. === Includes bibliographical references (leaves 105-109). === Abstracts in English and Chinese. === Abstract --- p.i === Acknowledgements --- p.iii === Introduction --- p.1 === Chapter 1 --- Morse Theory --- p.4 === Chapter 1.1 --- Introduction --- p.4 === Chapter 1.2 --- Morse Homology --- p.11 === Chapter 2 --- Symplectic Fixed Points and Arnold Conjecture --- p.24 === Chapter 2.1 --- Introduction --- p.24 === Chapter 2.2 --- The Variational Approach --- p.29 === Chapter 2.3 --- Action Functional and Moduli Space --- p.30 === Chapter 2.4 --- Construction of Floer Homology --- p.42 === Chapter 3 --- Fredholm Theory --- p.46 === Chapter 3.1 --- Fredholm Operator --- p.47 === Chapter 3.2 --- The Linearized Operator --- p.48 === Chapter 3.3 --- Maslov Index --- p.50 === Chapter 3.4 --- Fredholm Index --- p.57 === Chapter 4 --- Floer Homology --- p.75 === Chapter 4.1 --- Transversality --- p.75 === Chapter 4.2 --- Compactness and Gluing --- p.76 === Chapter 4.3 --- Floer Homology --- p.88 === Chapter 4.4 --- Invariance of Floer Homology --- p.90 === Chapter 4.5 --- An Isomorphism Theorem --- p.98 === Chapter 4.6 --- Further Applications --- p.103 === Bibliography --- p.105