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Survey on Heegaard Floer homology.

Suen, Chun Kit Anthony. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 89-92). / Abstracts in English and Chinese. / Abstract --- p.iii / Abstract --- p.iv / Acknowledgements --- p.v / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Morse Homology --- p.5 / Chapter 2.1 --- Introduction --- p.5 / Chapter 2.2 --- Classical Morse Theory and Morse Functions --- p.5 / Chapter 2.3 --- Handlebody Decomposition for 3-manifold --- p.7 / Chapter 2.4 --- Stable manifold and Unstable manifold --- p.10 / Chapter 2.5 --- Trajectory flows and the Morse-Smale-Witten Complex --- p.11 / Chapter 3 --- Lagrangian Floer Homology --- p.22 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- Preliminaries on Symplectic Geometry --- p.23 / Chapter 3.2.1 --- Basic Definitions --- p.23 / Chapter 3.2.2 --- The Symplectic Group --- p.26 / Chapter 3.2.3 --- Maslov index for non-degenerate paths in Sp(2n) --- p.28 / Chapter 3.2.4 --- Maslov index - the analytic aspect --- p.35 / Chapter 3.3 --- Definition of Floer Homology --- p.37 / Chapter 3.4 --- Some Remarks --- p.41 / Chapter 4 --- Heegaard Floer Homology --- p.43 / Chapter 4.1 --- Introduction --- p.43 / Chapter 4.2 --- Basic Set-Up --- p.43 / Chapter 4.3 --- Topological Preliminaries --- p.44 / Chapter 4.3.1 --- Symmetric Product --- p.44 / Chapter 4.3.2 --- The Tori Tα and Tβ --- p.47 / Chapter 4.3.3 --- Intersection Points and Disks --- p.48 / Chapter 4.3.4 --- Domains --- p.52 / Chapter 4.3.5 --- Spinc Structures --- p.54 / Chapter 4.3.6 --- Holomorphic Disks and Maslov Index --- p.63 / Chapter 4.4 --- Definition of Heegaard Floer Homology --- p.65 / Chapter 4.4.1 --- The chain complex CF --- p.66 / Chapter 4.4.2 --- The chain complex CF∞ --- p.67 / Chapter 4.4.3 --- The chain complexes CF+ and CF- --- p.68 / Chapter 4.4.4 --- Some Remarks --- p.70 / Chapter 5 --- Examples and Applications --- p.72 / Chapter 5.1 --- Introduction --- p.72 / Chapter 5.2 --- The homology three-spheres --- p.72 / Chapter 5.2.1 --- The sphere S3 --- p.72 / Chapter 5.2.2 --- The Poincare sphere and the Brieskorn spheres --- p.74 / Chapter 5.2.3 --- Long exact surgery sequence and the absolutely graded Hee- gaard Floer homology --- p.78 / Chapter 5.3 --- More Application --- p.84 / Chapter 5.3.1 --- Knot Floer homology --- p.84 / Chapter 5.3.2 --- Invariants on 4-manifolds --- p.86 / Chapter 5.4 --- Further developments --- p.87 / Bibliography --- p.89

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326217
Date January 2007
ContributorsSuen, Chun Kit Anthony., Chinese University of Hong Kong Graduate School. Division of Mathematics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, 92 leaves : ill. ; 30 cm.
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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