Return to search

A survey of Seiberg-Witten theory and its applications to 4-manifolds.

Chan, Kai Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 106-109). / Abstracts in English and Chinese. / Chapter 0 --- Introduction --- p.7 / Chapter I --- Background Scenery --- p.10 / Chapter 1 --- Seiberg-Witten Invariants --- p.11 / Chapter 1.1 --- Preliminaries --- p.11 / Chapter 1.2 --- Construction of Seiberg-Witten Invariants --- p.17 / Chapter 1.2.1 --- Seiberg-Witten Equations and the Moduli Space --- p.17 / Chapter 1.2.2 --- Seiberg-Witten Invariants --- p.19 / Chapter 1.2.3 --- Remarks --- p.20 / Chapter 1.2.4 --- Seiberg-Witten Invariants for b+2= 1 --- p.22 / Chapter 1.3 --- Important Results of Seiberg-Witten Invariants --- p.23 / Chapter 1.3.1 --- Manifolds Admit Positive Scalar Metrics --- p.23 / Chapter 1.3.2 --- Connected Sums --- p.25 / Chapter 1.3.3 --- Kahler Surfaces --- p.27 / Chapter 1.3.4 --- Symplectic Manifolds --- p.30 / Chapter 2 --- Intersection Forms --- p.32 / Chapter 2.1 --- Intersection Forms of 4-manifolds --- p.32 / Chapter 2.2 --- Classification Theorem --- p.34 / Chapter 2.3 --- Review: Van Kampen's Theorem --- p.35 / Chapter 3 --- Kirby Calculus --- p.37 / Chapter 3.1 --- Review on Handle Decompositions --- p.37 / Chapter 3.1.1 --- Constructions --- p.38 / Chapter 3.1.2 --- Handle Slides and Cancellations --- p.42 / Chapter 3.1.3 --- Calculation of Homology Groups --- p.44 / Chapter 3.2 --- Kirby Diagrams --- p.45 / Chapter 3.2.1 --- Constructions --- p.45 / Chapter 3.2.2 --- Handle Slides and Cancellations --- p.50 / Chapter 3.2.3 --- Dotted Notation for 1-handles --- p.56 / Chapter 3.3 --- 3-Manifolcis: As Boundaries of 4-Manifolds --- p.60 / Chapter 3.3.1 --- Introduction --- p.60 / Chapter 3.3.2 --- Lens spaces --- p.62 / Chapter 3.4 --- Linear Plumbing --- p.63 / Chapter 3.5 --- Rational Blowdown --- p.65 / Chapter II --- Examples of Exotic Structures --- p.71 / Chapter 4 --- mCP2#kCP2 --- p.72 / Chapter 4.1 --- Introduction --- p.72 / Chapter 4.2 --- Example: CP2#7CP2 --- p.73 / Chapter 4.3 --- Progress of Researches --- p.85 / Chapter 5 --- Gluing Results in Seiberg-Witten Theory --- p.89 / Chapter 5.1 --- Revisit of Seiberg-Witten Invariants --- p.89 / Chapter 5.2 --- Fiber Sums and its Generalization --- p.91 / Chapter 5.3 --- Logarithmic transformations and its Generalization --- p.93 / Chapter 5.4 --- Knot Theory and Alexander Polynomials --- p.96 / Chapter 5.5 --- Main Theorem --- p.102 / Bibliography --- p.106

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326098
Date January 2007
ContributorsChan, Kai Leung., Chinese University of Hong Kong Graduate School. Division of Mathematics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, 109 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/)

Page generated in 0.0024 seconds