Survey on Heegaard Floer homology.

• Other Authors: Suen, Chun Kit Anthony.
• Format: Others
• Language: English; Chinese
• Published: 2007
• Subjects: Homology theory; Three-manifolds (Topology)
• Online Access: http://library.cuhk.edu.hk/record=b5893485; http://repository.lib.cuhk.edu.hk/en/item/cuhk-326217

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