No description available.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2005. / Includes bibliographical references (leaves 75-79). Also available in electronic version.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas, Programa de Pós-Graduação em Matemática Pura e Aplicada, Florianópolis, 2015. / Made available in DSpace on 2016-04-15T13:14:32Z (GMT). No. of bitstreams: 1 337664.pdf: 536732 bytes, checksum: 05d9bcd03f63abedc6424dd86afdfef7 (MD5) Previous issue date: 2015 / Orbifolds podem ser vistos como generalizac¸oes de variedades. Podemos defini-los por cartas e atlas, quocientes de variedades por ações de grupos ou grupoides de Lie. Nosso objetivo neste trabalho e caracterizá-los por estas maneiras distintas e ver as relações existentes entre cada definição.<br> / Abstract : Orbifolds can be seen as generalizations of manifolds. We can define them through charts and atlases, quotients of manifolds by group actions or Lie groupoids. Our goal in this work is to study these different approaches characterize them accordingly and see the relationships between these settings.

Abstract Not Provided. / Thesis / Master of Science (MSc)

This thesis examines orbifold versions of three results concerning the existence of canonical metrics in the Kahler setting. The first of these is Yau's solution to Calabi's conjecture, which demonstrates the existence of a Kahler metric with prescribed Ricci form on a compact Kahler manifold. The second is a variant of Yau's solution in a certain non-compact setting, namely, the setting in which the Kahler manifold is assumed to be asymptotic to a cone. The final result is one due to Uhlenbeck and Yau which asserts the existence of Kahler-Einstein metrics on stable vector bundles over compact Kahler manifolds.

The computer programs SnapPea by Weeks and Geo by Casson have proven to be powerful tools in the study of hyperbolic 3-manifolds. Manifolds are special examples of spaces called orbifolds, which are modelled locally on R^n modulo finite groups of symmetries. SnapPea can also be used to study orbifolds but it is restricted to those whose singular set is a link.One goal of this thesis is to lay down the theory for a computer program that can work on a much larger class of 3-orbifolds. The work of Casson is generalized and implemented in a computer program Orb which should provide new insight into hyperbolic 3-orbifolds.The other main focus of this work is the study of 2-handle additions. Given a compact 3-manifold M and an essential simple closed curve α on ∂M, then we define M[α] to be the manifold obtained by gluing a 2-handle to ∂M along α. If α lies on a torus boundary component, we cap off the spherical boundary component created and the result is just Dehn filling.The case when α lies on a boundary surface of genus ≥ 2 is examined and conditions on α guaranteeing that M[α] is hyperbolic are found. This uses a lemma of Scharlemann and Wu, an argument of Lackenby, and a theorem of Marshall and Martin on the density of strip packings. A method for performing 2-handle additions is then described and employed to study two examples in detail.This thesis concludes by illustrating applications of Orb in studying orbifoldsand in the classification of knotted graphs. Hyperbolic invariants are used to distinguish the graphs in Litherland’s table of 90 prime θ-curves and provide access to new topological information including symmetry groups. Then by prescribing cone angles along the edges of knotted graphs, tables of low volume orbifolds are produced.

[pt] Iniciamos com o estudo das orbifolds, que são espaços topológicos localmente homeomorfos a quocientes de Rn por grupos finitos. Estudamos em seguida os fibrados de Seifert de dimensão três, que consistem-se de folheações por círculos que podem ser vistas como fibrados sobre orbifolds. Esse material é usado em seguida no estudo das geometrias modelo. Uma geometria modelo (ou geometria de Thurston) é um par (G;X), onde X é uma variedade conexa e simplesmente conexa e G é um grupo de difeomorfismos de X com certas propriedades que nos permite encontrar uma métrica riemanniana em X tal que G é o grupo de todas as isometrias. A classificação das geometrias modelo é muito útil na classificação topológica das variedades que admitem uma métrica localmente homogênea e foi feita por Thurston em Three-Dimensional Geometry and Topology, vol.1, Princeton University Press, 1997. Na seqüência, apresentamos uma breve descrição de cada geometria modelo bem como parte da prova do teorema de classificação das geometrias modelo. / [en] We begin by studying orbifolds, i.e., topological spaces locally homeomorphic to quotients of Rn by finite groups. Then we study Seifert fiber spaces of dimension three which are certain type of foliations by circles that can be seen as fiber bundles over orbifolds. This material is useful in the subsequent study of Thurston model geometries. A Thurston model geometry is a pair (G;X), where X is a connected and simply connected manifold and G is a group of diffeomorfisms of X with certain properties that allow us to find a riemannian metric on X such that G is the group of all isometries. The classification of the model geometries is very useful in the topological classification of manifolds that admit a locally-homogeneous metric and was done by Thurston in Three-Dimensional Geometry and Topology, vol.1, Princeton University Press, 1997. Then we give a brief description of each one of these eight geometries and present part of Thurston s classification theorem.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, Dept. of Physics, Dec. 2003. / Includes bibliographical references. Also available on the Internet.

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