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Lectures on Coarse Geometry

Lectures on Coarse Geometry Author John Roe
ISBN-10 9780821833322
Release 2003
Pages 175
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Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry: two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section of the book reviews notions of negative curvature and rigidity.Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of negatively curved spaces. The final chapters discuss recent results on asymptotic dimension and uniform embeddings into Hilbert space. John Roe is known for his work on index theory, coarse geometry, and topology. His exposition is clear and direct, bringing insight to this modern field of mathematics. Students and researchers who wish to learn about contemporary methods of understanding the geometry and topology of manifolds will be well served by reading this book. Also available from the AMS by John Roe is ""Index Theory, Coarse Geometry, and Topology of Manifolds"".



Noncommutative Geometry and Physics 3

Noncommutative Geometry and Physics 3 Author Giuseppe Dito
ISBN-10 9789814425018
Release 2013
Pages 536
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Noncommutative differential geometry has many actual and potential applications to several domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field.



Limits of Graphs in Group Theory and Computer Science

Limits of Graphs in Group Theory and Computer Science Author Goulnara Arzhantseva
ISBN-10 1439804001
Release 2009-03-16
Pages 285
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A collection of research articles and survey papers, this text highlights current methods and open problems in the geometric, combinatorial, and computational aspects of group theory. New interactions with broad areas of theoretical computer science are also considered. Pub 3/09.



Noncommutative Geometry and Physics 3

Noncommutative Geometry and Physics 3 Author Giuseppe Dito
ISBN-10 9789814425025
Release 2013-01-11
Pages 536
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Noncommutative differential geometry is a novel approach to geometry, aimed in part at applications in physics. It was founded in the early eighties by the 1982 Fields Medalist Alain Connes on the basis of his fundamental works in operator algebras. It is now a very active branch of mathematics with actual and potential applications to a variety of domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field. It is an important topic both for mathematics and physics. Contents:K-Theory and D-Branes, Shonan:The Local Index Formula in Noncommutative Geometry Revisited (Alan L Carey, John Phillips, Adam Rennie and Fedor A Sukochev)Semi-Finite Noncommutative Geometry and Some Applications (Alan L Carey, John Phillips and Adam Rennie)Generalized Geometries in String Compactification Scenarios (Tetsuji Kimura)What Happen to Gauge Theories under Noncommutative Deformation? (Akifumi Sako)D-Branes and Bivariant K-Theory (Richard J Szabo)Two-Sided Bar Constructions for Partial Monoids and Applications to K-Homology Theory (Dai Tamaki)Twisting Segal's K-Homology Theory (Dai Tamaki)Spectrum of Non-Commutative Harmonic Oscillators and Residual Modular Forms (Kazufumi Kimoto and Masato Wakayama)Coarse Embeddings and Higher Index Problems for Expanders (Qin Wang)Deformation Quantization and Noncommutative Geometry, RIMS:Enriched Fell Bundles and Spaceoids (Paolo Bertozzini, Roberto Conti and Wicharn Lewkeeratiyutkul)Weyl Character Formula in KK-Theory (Jonathan Block and Nigel Higson)Recent Advances in the Study of the Equivariant Brauer Group (Peter Bouwknegt, Alan Carey and Rishni Ratnam)Entire Cyclic Cohomology of Noncommutative Manifolds (Katsutoshi Kawashima)Geometry of Quantum Projective Spaces (Francesco D'Andrea and Giovanni Landi)On Yang–Mills Theory for Quantum Heisenberg Manifolds (Hyun Ho Lee)Dilatational Equivalence Classes and Novikov–Shubin Type Capacities of Groups, and Random Walks (Shin-ichi Oguni)Deformation Quantization of Gauge Theory in ℝ4 and U(1) Instanton Problems (Yoshiaki Maeda and Akifumi Sako)Dualities in Field Theories and the Role of K-Theory (Jonathan Rosenberg)Dualities in Field Theories and the Role of K-Theory (Jonathan Rosenberg) Readership: Researchers and graduate students in Mathematical Physics and Applied Mathematics. Keywords:Noncommutative Geometry;Deformation Quantizations;D-Brane;K-Theory;T-Duality



Global Differential Geometry

Global Differential Geometry Author Christian Bär
ISBN-10 9783642228421
Release 2011-12-18
Pages 524
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This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.



European Congress of Mathematics

European Congress of Mathematics Author Ari Laptev
ISBN-10 3037190094
Release 2005-01-01
Pages 879
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European Congress of Mathematics has been writing in one form or another for most of life. You can find so many inspiration from European Congress of Mathematics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full European Congress of Mathematics book for free.



In the Tradition of Ahlfors Bers IV

In the Tradition of Ahlfors Bers  IV Author Richard Douglas Canary
ISBN-10 9780821842270
Release 2007
Pages 229
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The Ahlfors-Bers Colloquia commemorate the mathematical legacy of Lars Ahlfors and Lipman Bers. The core of this legacy lies in the fields of geometric function theory, Teichmuller theory, hyperbolic manifolds, and partial differential equations. However, the work of Ahlfors and Bers has impacted and created interactions with many other fields, such as algebraic geometry, mathematical physics, dynamics, geometric group theory, number theory, and topology. The triannual Ahlford-Bers colloquia serve as a venue to disseminate the relevant work to the wider mathematical community and bring the key participants together to ponder future directions in the field. The present volume includes a wide range of articles in the fields central to this legacy. The majority of articles present new results, but there are expository articles as well.



Index Theory Coarse Geometry and Topology of Manifolds

Index Theory  Coarse Geometry  and Topology of Manifolds Author John Roe
ISBN-10 9780821804131
Release 1996
Pages 100
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Lecture notes from the conference held Aug. 1995 in Boulder, Colo.



Metric and Comparison Geometry

Metric and Comparison Geometry Author Jeff Cheeger
ISBN-10 1571461175
Release 2007
Pages 347
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Metric and Comparison Geometry has been writing in one form or another for most of life. You can find so many inspiration from Metric and Comparison Geometry also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Metric and Comparison Geometry book for free.



Annales Scientifiques de L cole Normale Sup rieure

Annales Scientifiques de L   cole Normale Sup  rieure Author
ISBN-10 UOM:39015072641379
Release 2008
Pages
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Annales Scientifiques de L cole Normale Sup rieure has been writing in one form or another for most of life. You can find so many inspiration from Annales Scientifiques de L cole Normale Sup rieure also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Annales Scientifiques de L cole Normale Sup rieure book for free.



Geometry Topology

Geometry   Topology Author
ISBN-10 UOM:39015072617262
Release 2007
Pages
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Fully refereed international journal dealing with all aspects of geometry and topology and their applications.



Mathematical Reviews

Mathematical Reviews Author
ISBN-10 UOM:39015059777659
Release 2004
Pages
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Mathematical Reviews has been writing in one form or another for most of life. You can find so many inspiration from Mathematical Reviews also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mathematical Reviews book for free.



Revista Matem tica Iberoamericana

Revista Matem  tica Iberoamericana Author
ISBN-10 UOM:39015081659065
Release 2008
Pages
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Revista Matem tica Iberoamericana has been writing in one form or another for most of life. You can find so many inspiration from Revista Matem tica Iberoamericana also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Revista Matem tica Iberoamericana book for free.



Large Scale Geometry

Large Scale Geometry Author Piotr W. Nowak
ISBN-10 3037191120
Release 2012
Pages 189
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Large Scale Geometry has been writing in one form or another for most of life. You can find so many inspiration from Large Scale Geometry also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Large Scale Geometry book for free.



American Book Publishing Record

American Book Publishing Record Author
ISBN-10 UOM:39015066043152
Release 2003
Pages
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American Book Publishing Record has been writing in one form or another for most of life. You can find so many inspiration from American Book Publishing Record also informative, and entertaining. Click DOWNLOAD or Read Online button to get full American Book Publishing Record book for free.



From Groups to Geometry and Back

From Groups to Geometry and Back Author Vaughn Climenhaga
ISBN-10 9781470434793
Release 2017-04-07
Pages 420
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Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth. The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness. This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009.



Noncommutative Geometry

Noncommutative Geometry Author Alain Connes
ISBN-10 9780080571751
Release 1995-01-17
Pages 661
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This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields. Key Features * First full treatment of the subject and its applications * Written by the pioneer of this field * Broad applications in mathematics * Of interest across most fields * Ideal as an introduction and survey * Examples treated include: @subbul* the space of Penrose tilings * the space of leaves of a foliation * the space of irreducible unitary representations of a discrete group * the phase space in quantum mechanics * the Brillouin zone in the quantum Hall effect * A model of space time