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
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326217 |
| Date | January 2007 |
| Contributors | Suen, Chun Kit Anthony., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, 92 leaves : ill. ; 30 cm. |
| Rights | Use 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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