Local Collapsing Orbifolds And Geometrization
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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.
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.
Ricci Flow And Geometric Applications
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Author : Michel Boileau
language : en
Publisher: Springer
Release Date : 2016-09-09
Ricci Flow And Geometric Applications written by Michel Boileau and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-09 with Mathematics categories.
Presenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow. These ideas are at the core of the study of differentiable manifolds. Several very important open problems and conjectures come from this area and the techniques described herein are used to face and solve some of them. The book’s four chapters are based on lectures given by leading researchers in the field of geometric analysis and low-dimensional geometry/topology, respectively offering an introduction to: the differentiable sphere theorem (G. Besson), the geometrization of 3-manifolds (M. Boileau), the singularities of 3-dimensional Ricci flows (C. Sinestrari), and Kähler–Ricci flow (G. Tian). The lectures will be particularly valuable to young researchers interested in differential manifolds.
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.
A Torsion Jacquet Langlands Correspondence
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Author : Frank Calegari
language : en
Publisher:
Release Date : 2019
A Torsion Jacquet Langlands Correspondence written by Frank Calegari and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Algebra, Homological categories.
"We prove a numerical form of a Jacquet-Langlands correspondence for torsion classes on arithmetic hyperbolic 3-manifolds." -- Prové de l'editor.
A New Approach To Kazhdan Lusztig Theory Of Type B Via Quantum Symmetric Pairs
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Author : Huanchen Bao
language : en
Publisher:
Release Date : 2018
A New Approach To Kazhdan Lusztig Theory Of Type B Via Quantum Symmetric Pairs written by Huanchen Bao and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Hecke algebras categories.
We show that Hecke algebra of type B and a coideal subalgebra of the type A quantum group satsify a double centralizer property, generalizing the Schur-Jimbo duality in type A. The quantum group of type A and its coideal subalgebra form a quantum symmetric pair. A new theory of canonical bases arising from quantum symmetric pairs is initiated. It is then applied to formulate and establish for the first time a Kazhdan-Lusztig theory for the BGG category [O] of the orthosymplectic Lie superalgebras osp(2m + 1[vertical bar]2n). In particular, our approach provides a new formulation of the Kazhdan-Lusztig theory for Lie algebras of type B/C.
Ricci Solitons In Low Dimensions
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Author : Bennett Chow
language : en
Publisher: American Mathematical Society
Release Date : 2023-10-04
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 2023-10-04 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.
Geometrisation Of 3 Manifolds
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Author :
language : en
Publisher: European Mathematical Society
Release Date : 2010
Geometrisation Of 3 Manifolds written by and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Covering spaces (Topology) categories.
The Geometrisation Conjecture was proposed by William Thurston in the mid 1970s in order to classify compact 3-manifolds by means of a canonical decomposition along essential, embedded surfaces into pieces that possess geometric structures. It contains the famous Poincaré Conjecture as a special case. In 2002, Grigory Perelman announced a proof of the Geometrisation Conjecture based on Richard Hamilton’s Ricci flow approach, and presented it in a series of three celebrated arXiv preprints. Since then there has been an ongoing effort to understand Perelman’s work by giving more detailed and accessible presentations of his ideas or alternative arguments for various parts of the proof. This book is a contribution to this endeavour. Its two main innovations are first a simplified version of Perelman’s Ricci flow with surgery, which is called Ricci flow with bubbling-off, and secondly a completely different and original approach to the last step of the proof. In addition, special effort has been made to simplify and streamline the overall structure of the argument, and make the various parts independent of one another. A complete proof of the Geometrisation Conjecture is given, modulo pre-Perelman results on Ricci flow, Perelman’s results on the ℒ-functional and κ-solutions, as well as the Colding–Minicozzi extinction paper. The book can be read by anyone already familiar with these results, or willing to accept them as black boxes. The structure of the proof is presented in a lengthy introduction, which does not require knowledge of geometric analysis. The bulk of the proof is the existence theorem for Ricci flow with bubbling-off, which is treated in parts I and II. Part III deals with the long time behaviour of Ricci flow with bubbling-off. Part IV finishes the proof of the Geometrisation Conjecture.
S Minaire Bourbaki
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Author : Société mathématique de France
language : fr
Publisher:
Release Date : 2019
S Minaire Bourbaki written by Société mathématique de France and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Algebraic topology categories.
"This 69th volume of the Bourbaki Seminar contains the texts of the fifteen survey lectures done during the year 2016/2017. Topics addressed covered Langlands correspondence, NIP property in model theory, Navier-Stokes equation, algebraic and complex analytic geometry, algorithmic and geometric questions in knot theory, analytic number theory formal moduli problems, general relativity, sofic entropy, sphere packings, subriemannian geometry." -- Prové de l'editor.
Lectures On Spaces Of Nonpositive Curvature
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Author : Werner Ballmann
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Lectures On Spaces Of Nonpositive Curvature written by Werner Ballmann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the Hadamard-Cartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha Brin, a self-contained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the non-specialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory.