Chan, Kin Wai. / "September 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 103-106). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.8 / Chapter 2 --- Background Knowledge --- p.13 / Chapter 2.1 --- Results from Riemann Surface Theory and Quasicon- formal Mappings --- p.13 / Chapter 2.1.1 --- Riemann Surfaces and the Uniformization The- orem --- p.13 / Chapter 2.1.2 --- Fuchsian Groups --- p.15 / Chapter 2.1.3 --- Quasiconformal Mappings and the Beltrami Equation --- p.17 / Chapter 2.1.4 --- Holomorphic Quadratic Differentials --- p.20 / Chapter 2.1.5 --- Nodal Riemann Surfaces --- p.21 / Chapter 2.2 --- Teichmuller Theory --- p.24 / Chapter 2.2.1 --- Teichmiiller Spaces --- p.24 / Chapter 2.2.2 --- Teichmuller's Distance --- p.26 / Chapter 2.2.3 --- The Bers Embedding --- p.26 / Chapter 2.2.4 --- Teichmuller Modular Groups and Moduli Spaces of Riemann Surfaces --- p.27 / Chapter 2.2.5 --- Infinitesimal Theory of Teichmiiller Spaces --- p.28 / Chapter 2.2.6 --- Boundary of Moduli Spaces of Riemann Sur- faces --- p.29 / Chapter 2.3 --- Schwarz-Yau Lemma --- p.30 / Chapter 3 --- Classical Canonical Metrics on the Teichnmuller Spaces and the Moduli Spaces of Riemann Surfaces --- p.31 / Chapter 3.1 --- Finsler Metrics and Bergman Metric --- p.31 / Chapter 3.1.1 --- Definitions and Properties of the Metrics --- p.32 / Chapter 3.1.2 --- Equivalences of the Metrics --- p.33 / Chapter 3.2 --- Weil-Petersson Metric --- p.36 / Chapter 3.2.1 --- Definition and Properties of the Weil-Petersson Metric --- p.36 / Chapter 3.2.2 --- Results about Harmonic Lifts --- p.37 / Chapter 3.2.3 --- Curvature Formula for the Weil-Petersson Met- ric --- p.41 / Chapter 4 --- Kahler Metrics on the Teichmiiller Spaces and the Moduli Spaces of Riemann Surfaces --- p.42 / Chapter 4.1 --- McMullen Metric --- p.42 / Chapter 4.1.1 --- Definition of the McMullen Metric --- p.42 / Chapter 4.1.2 --- Properties of the McMullen Metric --- p.43 / Chapter 4.1.3 --- Equivalence of the McMullen Metric and the Teichmuller Metric --- p.45 / Chapter 4.2 --- Kahler-Einstein Metric --- p.50 / Chapter 4.2.1 --- Existence of the Kahler-Einstein Metric --- p.50 / Chapter 4.2.2 --- A Conjecture of Yau --- p.50 / Chapter 4.3 --- Ricci Metric --- p.51 / Chapter 4.3.1 --- Definition of the Ricci Metric --- p.51 / Chapter 4.3.2 --- Curvature Formula of the Ricci Metric --- p.53 / Chapter 4.4 --- The Asymptotic Behavior of the Ricci Metric --- p.61 / Chapter 4.4.1 --- Estimates on the Asymptotics of the Ricci Metric --- p.61 / Chapter 4.4.2 --- Estimates on the Curvature of the Ricci Metric --- p.83 / Chapter 4.5 --- Perturbed Ricci Metric --- p.92 / Chapter 4.5.1 --- Definition and the Curvature Formula of the Perturbed Ricci Metric --- p.92 / Chapter 4.5.2 --- Estimates on the Curvature of the Perturbed Ricci Metric --- p.93 / Chapter 4.5.3 --- Equivalence of the Perturbed Ricci Metric and the Ricci Metric --- p.96 / Chapter 5 --- Equivalence of the Kahler Metrics on the Teichmuller Spaces and the Moduli Spaces of Riemann Surfaces --- p.98 / Chapter 5.1 --- Equivalence of the Ricci Metric and the Kahler-Einstein Metric --- p.98 / Chapter 5.2 --- Equivalence of the Ricci Metric and the McMullen Metric --- p.99 / Bibliography --- p.103

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 61-64). Available also in a digital version from Dissertation Abstracts.

No description available.

Thesis (Ph.D.)--McMaster University (Canada), 1995. / Source: Dissertation Abstracts International, Volume: 57-10, Section: B, page: 6295. Adviser: I. Hambleton.

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 44-48).

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 20-21). Also available in electronic version. Access restricted to campus users.

Thesis (doctoral)--Bonn, 1998. / Pages 10, 68 and 102 blank. Includes bibliographical references (p. 103-105).

by Wong Chun-fai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 81-82). / Chapter CHAPTER0 --- Introduction --- p.1 / Chapter CHAPTER1 --- Teichmuller Space of genus g --- p.5 / Chapter 1.1. --- Teichmiiller Space of genus g / Chapter 1.2. --- Fuchsian Model and Discrete subgroup of Aut(H) / Chapter 1.3. --- Fricke Space / Chapter CHAPTER2 --- Hyperbolic Geometry and Fenchel-Nielsen Coordinates --- p.14 / Chapter 2.1. --- Poincare Metric and Hyperbolic Geometry / Chapter 2.2. --- Fenchel-Nielsen Coordinates / Chapter 2.3. --- Fricke-Klein Embedding / Chapter CHAPTER3 --- Quasiconformal Mappings --- p.23 / Chapter 3.1. --- Definitions / Chapter 3.2. --- Existence Theorems on Quasiconformal Mappings / Chapter 3.3. --- Dependence on Beltrami Coefficients / Chapter CHAPTER4 --- Teichmuller Spaces --- p.37 / Chapter 4.1. --- Analytic Construction of Teichmiiller Spaces / Chapter 4.2. --- Teichmiiller mapping and Teichmiiller Theorem / Chapter 4.3. --- Teichmiiller Uniqueness Theorem / Chapter CHAPTER5 --- Complex Analytic Theory of Teichmiiller Spaces --- p.50 / Chapter 5.1. --- Bers' Embedding and the complex structure of Teichmiiller Space / Chapter 5.2. --- Invariance of Complex Structure of Teichmiiller Space / Chapter 5.3. --- Teichmiiller Modular Groups / Chapter 5.4. --- Classification of Teichmiiller Modular Transformations / Chapter CHAPTER6 --- Weil-Petersson Metric --- p.68 / Chapter 6.1. --- Petersson Scalar Product and Reproducing formula / Chapter 6.2. --- Infinitesimal Theory of Teichmuller Spaces / Chapter 6.3. --- Weil-Petersson Metric / BIBLIOGRAPHY --- p.81

Kuranishi atlases were introduced by McDuff and Wehrheim as a means to build a virtual fundamental cycle on moduli spaces of J-holomorphic curves and resolve some of the challenges in this field. This thesis considers genus zero Gromov-Witten invariants on a general closed symplectic manifold. We complete the construction of these invariants using Kuranishi atlases. To do so, we show that Gromov-Witten moduli spaces admit a smooth enough Kuranishi atlas to define a virtual fundamental class in any virtual dimension. In the process, we prove a stronger gluing theorem. Once we have defined genus zero Gromov-Witten invariants, we show that they satisfy the Gromov-Witten axioms of Kontsevich and Manin, a series of main properties that these invariants are expected to satisfy. A key component of this is the introduction of the notion of a transverse subatlas, a useful tool for working with Kuranishi atlases.

The context of this thesis is derived categories in algebraic geometry and geo- metric quotients. Specifically, we prove the embedding of the derived category of a smooth curve of genus greater than one into the derived category of the moduli space of semistable pairs over the curve. We also describe closed cover conditions under which the composition of a pullback and a pushforward induces a fully faithful functor. To prove our main result, we give an exposition of how to think of general Geometric Invariant Theory quotients as quotients by the multiplicative group.