Three Dimensional Orbifolds And Cone Manifolds
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Three Dimensional Orbifolds And Cone Manifolds
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Author : Daryl Cooper
language : en
Publisher:
Release Date : 2000
Three Dimensional Orbifolds And Cone Manifolds written by Daryl Cooper and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Manifolds (Mathematics) categories.
This volume provides an excellent introduction of the statement and main ideas in the proof of the orbifold theorem announced by Thurston in late 1981. It is based on the authors' lecture series entitled "Geometric Structures on 3-Dimensional Orbifolds" which was featured in the third MSJ Regional Workshop on "Cone-Manifolds and Hyperbolic Geometry" held on July 1-10, 1998, at Tokyo Institute of Technology. The orbifold theorem shows the existence of geometric structures on many 3-orbifolds and on 3-manifolds with symmetry. The authors develop the basic properties of orbifolds and cone-manifolds, extends many ideas from the differential geometry to the setting of cone-manifolds and outlines a proof of the orbifold theorem.
Three Dimensional Orbifolds And Their Geometric Structures
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Author : Michel Boileau
language : en
Publisher:
Release Date : 2003
Three Dimensional Orbifolds And Their Geometric Structures written by Michel Boileau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Orbifolds locally look like quotients of manifolds by finite group actions. They play an important role in the study of proper actions of discrete groups on manifolds. This monograph presents recent fundamental results on the geometry and topology of 3-dimensional orbifolds, with an emphasis on their geometric properties. It is suitable for graduate students and research mathematicians interested in geometry and topology.
Local Collapsing Orbifolds And Geometrization
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Author : Bruce Kleiner
language : en
Publisher:
Release Date : 2014
Local Collapsing Orbifolds And Geometrization written by Bruce Kleiner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Global differential geometry categories.
This volume has two papers which can be read separately. The first paper concerns local collapsing in Riemannian geometry. The authors prove that a three-dimensional compact Riemannian manifold which is locally collapsed, with respect to a lower curvature bound, is a graph manifold. This theorem was stated by Perelman without proof and was used in his proof of the geometrization conjecture. The second paper is about the geometrization of orbifolds. A three-dimensional closed orientable orbifold, which has no bad suborbifolds, is known to have a geometric decomposition. This is known from the work of Perelman in the manifold case, along with earlier work of Boileau-Leeb-Porti, Boileau-Maillot-Porti, Boileau-Porti, Cooper-Hodgson-Kerckhoff and Thurston. The authors give a new, logically independent, unified proof of the geometrization of orbifolds, using Ricci flow.
In The Tradition Of Thurston Ii
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Author : Ken’ichi Ohshika
language : en
Publisher: Springer Nature
Release Date : 2022-08-02
In The Tradition Of Thurston Ii written by Ken’ichi Ohshika and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-02 with Mathematics categories.
The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston’s heritage. Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The topics covered in the present volume include com-plex hyperbolic Kleinian groups, Möbius structures, hyperbolic ends, cone 3-manifolds, Thurston’s norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups.
All Compact Orientable Three Dimensional Manifolds Admit Total Foliations
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Author : Detlef Hardorp
language : en
Publisher: American Mathematical Soc.
Release Date : 1980
All Compact Orientable Three Dimensional Manifolds Admit Total Foliations written by Detlef Hardorp and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Foliations categories.
A total foliation is an example of a geometric structure on a manifold. A total foliation of an [script]n dimensional manifold consists of a [script]n codimension one foliations that are transverse at every point. If a manifold admits a total foliation where all [script]n foliations are transverse oriented, it is said to be totally parallelizable. A necessary condition for total parallelizability is that the manifold be parallelizable. Whether or not this is also a sufficient condition is not known. In this memoir, the author proves a theorem: All compact orientable three dimensional manifolds admit total foliations. This theorem is proven by explicitly constructing total foliations for all compact orientable three manifolds
Handbook Of Geometric Topology
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Author : R.B. Sher
language : en
Publisher: Elsevier
Release Date : 2001-12-20
Handbook Of Geometric Topology written by R.B. Sher and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-20 with Mathematics categories.
Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.
Current Trends In Analysis Its Applications And Computation
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Author : Paula Cerejeiras
language : en
Publisher: Springer Nature
Release Date : 2022-10-03
Current Trends In Analysis Its Applications And Computation written by Paula Cerejeiras and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-03 with Mathematics categories.
This volume contains the contributions of the participants of the 12th ISAAC congress which was held at the University of Aveiro, Portugal, from July 29 to August 3, 2019. These contributions originate from the following sessions: Applications of dynamical systems theory in biology, Complex Analysis and Partial Differential Equations, Complex Geometry, Complex Variables and Potential Theory, Constructive Methods in the Theory of Composite and Porous Media, Function Spaces and Applications, Generalized Functions and Applications, Geometric & Regularity Properties of Solutions to Elliptic and Parabolic PDEs, Geometries Defined by Differential Forms, Partial Differential Equations on Curved Spacetimes, Partial Differential Equations with Nonstandard Growth, Quaternionic and Clifford Analysis, Recent Progress in Evolution Equations, Wavelet theory and its Related Topics.
Interactions Between Hyperbolic Geometry Quantum Topology And Number Theory
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Author : Abhijit Champanerkar
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Interactions Between Hyperbolic Geometry Quantum Topology And Number Theory written by Abhijit Champanerkar and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This book is based on a 10-day workshop given by leading experts in hyperbolic geometry, quantum topology and number theory, in June 2009 at Columbia University. Each speaker gave a minicourse consisting of three or four lectures aimed at graduate students and recent PhDs. The proceedings of this enormously successful workshop can serve as an introduction to this active research area in a way that is expository and broadly accessible to graduate students. Although many ideas overlap, the twelve expository/research papers in this volume can be grouped into four rough categories: (1) different approaches to the Volume Conjecture, and relations between the main quantum and geometric invariants; (2) the geometry associated to triangulations of hyperbolic 3-manifolds; (3) arithmetic invariants of hyperbolic 3-manifolds; (4) quantum invariants associated to knots and hyperbolic 3-manifolds. The workshop, the conference that followed, and these proceedings continue a long tradition in quantum and geometric topology of bringing together ideas from diverse areas of mathematics and physics, and highlights the importance of collaborative research in tackling big problems that require expertise in disparate disciplines.
Kleinian Groups And Hyperbolic 3 Manifolds
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Author : Y. Komori
language : en
Publisher: Cambridge University Press
Release Date : 2003-11-10
Kleinian Groups And Hyperbolic 3 Manifolds written by Y. Komori and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-10 with Mathematics categories.
The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development, with many old problems and conjectures close to resolution. This volume, proceedings of the Warwick workshop in September 2001, contains expositions of many of these breakthroughs including Minsky's lectures on the first half of the proof of the Ending Lamination Conjecture, the Bers Density Conjecture by Brock and Bromberg, the Tameness Conjecture by Kleineidam and Souto, the state of the art in cone manifolds by Hodgson and Kerckhoff, and the counter example to Thurston's K=2 conjecture by Epstein, Marden and Markovic. It also contains Jørgensen's famous paper 'On pairs of once punctured tori' in print for the first time. The excellent collection of papers here will appeal to graduate students, who will find much here to inspire them, and established researchers who will find this valuable as a snapshot of current research.
Ricci Solitons In Low Dimensions
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Author : Bennett Chow
language : en
Publisher: American Mathematical Society
Release Date : 2023-09-26
Ricci Solitons In Low Dimensions written by Bennett Chow and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-26 with Mathematics categories.
Ricci flow is an exciting subject of mathematics with diverse applications in geometry, topology, and other fields. It employs a heat-type equation to smooth an initial Riemannian metric on a manifold. The formation of singularities in the manifold's topology and geometry is a desirable outcome. Upon closer examination, these singularities often reveal intriguing structures known as Ricci solitons. This introductory book focuses on Ricci solitons, shedding light on their role in understanding singularity formation in Ricci flow and formulating surgery-based Ricci flow, which holds potential applications in topology. Notably successful in dimension 3, the book narrows its scope to low dimensions: 2 and 3, where the theory of Ricci solitons is well established. A comprehensive discussion of this theory is provided, while also establishing the groundwork for exploring Ricci solitons in higher dimensions. A particularly exciting area of study involves the potential applications of Ricci flow in comprehending the topology of 4-dimensional smooth manifolds. Geared towards graduate students who have completed a one-semester course on Riemannian geometry, this book serves as an ideal resource for related courses or seminars centered on Ricci solitons.