Amenable Groupoids

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
Page : 888 pages
File Size : 54,5 Mb
Release : 2007
Category : Mathematics
ISBN : 3037190558

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Handbook of Teichmüller Theory by Athanase Papadopoulos Pdf

This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.

Author : C. Anantharaman-Delaroche
Publisher : Unknown
Page : 484 pages
File Size : 51,8 Mb
Release : 1956
Category : Groupoids
ISBN : 04250818

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Amenable Groupoids by C. Anantharaman-Delaroche Pdf

Author : Geometry AMS-IMS-SIAM Joint Summer Research Conference on Groupoids in Analysis,Arlan Ramsay,Jean Renault,AMS-IMS-SIAM JOINT SUMMER RESEARCH CONFERENCE ON G,Geometry Ams-Ims-Siam Joint Summer Research Conference on Groupoids I
Publisher : American Mathematical Soc.
Page : 192 pages
File Size : 43,7 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821820421

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Groupoids in Analysis, Geometry, and Physics by Geometry AMS-IMS-SIAM Joint Summer Research Conference on Groupoids in Analysis,Arlan Ramsay,Jean Renault,AMS-IMS-SIAM JOINT SUMMER RESEARCH CONFERENCE ON G,Geometry Ams-Ims-Siam Joint Summer Research Conference on Groupoids I Pdf

Groupoids often occur when there is symmetry of a nature not expressible in terms of groups. Other uses of groupoids can involve something of a dynamical nature. Indeed, some of the main examples come from group actions. It should also be noted that in many situations where groupoids have been used, the main emphasis has not been on symmetry or dynamics issues. For example, a foliation is an equivalence relation and has another groupoid associated with it, called the holonomy groupoid. While the implicit symmetry and dynamics are relevant, the groupoid records mostly the structure of the space of leaves and the holonomy.More generally, the use of groupoids is very much related to various notions of orbit equivalence. The point of view that groupoids describe 'singular spaces' can be found in the work of A. Grothendieck and is prevalent in the non-commutative geometry of A. Connes. This book presents the proceedings from the Joint Summer Research Conference on 'Groupoids in Analysis, Geometry, and Physics' held in Boulder, CO. The book begins with an introduction to ways in which groupoids allow a more comprehensive view of symmetry than is seen via groups. Topics range from foliations, pseudo-differential operators, $KK$-theory, amenability, Fell bundles, and index theory to quantization of Poisson manifolds. Readers will find examples of important tools for working with groupoids. This book is geared to students and researchers. It is intended to improve their understanding of groupoids and to encourage them to look further while learning about the tools used.

Author : Alan Paterson
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217749

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Groupoids, Inverse Semigroups, and their Operator Algebras by Alan Paterson Pdf

In recent years, it has become increasingly clear that there are important connections relating three concepts -- groupoids, inverse semigroups, and operator algebras. There has been a great deal of progress in this area over the last two decades, and this book gives a careful, up-to-date and reasonably extensive account of the subject matter. After an introductory first chapter, the second chapter presents a self-contained account of inverse semigroups, locally compact and r-discrete groupoids, and Lie groupoids. The section on Lie groupoids in chapter 2 contains a detailed discussion of groupoids particularly important in noncommutative geometry, including the holonomy groupoids of a foliated manifold and the tangent groupoid of a manifold. The representation theories of locally compact and r-discrete groupoids are developed in the third chapter, and it is shown that the C*-algebras of r-discrete groupoids are the covariance C*-algebras for inverse semigroup actions on locally compact Hausdorff spaces. A final chapter associates a universal r-discrete groupoid with any inverse semigroup. Six subsequent appendices treat topics related to those covered in the text. The book should appeal to a wide variety of professional mathematicians and graduate students in fields such as operator algebras, analysis on groupoids, semigroup theory, and noncommutative geometry. It will also be of interest to mathematicians interested in tilings and theoretical physicists whose focus is modeling quasicrystals with tilings. An effort has been made to make the book lucid and 'user friendly"; thus it should be accessible to any reader with a basic background in measure theory and functional analysis.

Author : C. Anantharaman-Delaroche,Jean Renault
Publisher : Unknown
Page : 200 pages
File Size : 55,5 Mb
Release : 2000
Category : C*-algebras
ISBN : UVA:X006111404

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Amenable Groupoids by C. Anantharaman-Delaroche,Jean Renault Pdf

Author : Dana P. Williams
Publisher : American Mathematical Soc.
Page : 398 pages
File Size : 43,5 Mb
Release : 2019-09-24
Category : C*-algebras
ISBN : 9781470451332

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Tool Kit for Groupoid C∗ -Algebras by Dana P. Williams Pdf

The construction of a C∗-algebra from a locally compact groupoid is an important generalization of the group C∗-algebra construction and of the transformation group C∗-algebra construction. Since their introduction in 1980, groupoid C∗-algebras have been intensively studied with diverse applications, including graph algebras, classification theory, variations on the Baum-Connes conjecture, and noncommutative geometry. This book provides a detailed introduction to this vast subject and is suitable for graduate students or any researcher who wants to use groupoid C∗-algebras in their work. The main focus is to equip the reader with modern versions of the basic technical tools used in the subject, which will allow the reader to understand fundamental results and make contributions to various areas in the subject. Thus, in addition to covering the basic properties and construction of groupoid C∗-algebras, the focus is to give a modern treatment of some of the major developments in the subject in recent years, including the Equivalence Theorem and the Disintegration Theorem. Also covered are the complicated subjects of amenability of groupoids and simplicity results. The book is reasonably self-contained and accessible to graduate students with a good background in operator algebras.

Author : Aidan Sims,Gábor Szabó,Dana Williams
Publisher : Springer Nature
Page : 163 pages
File Size : 52,8 Mb
Release : 2020-06-22
Category : Mathematics
ISBN : 9783030397135

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Operator Algebras and Dynamics: Groupoids, Crossed Products, and Rokhlin Dimension by Aidan Sims,Gábor Szabó,Dana Williams Pdf

This book collects the notes of the lectures given at the Advanced Course on Crossed Products, Groupoids, and Rokhlin dimension, that took place at the Centre de Recerca Matemàtica (CRM) from March 13 to March 17, 2017. The notes consist of three series of lectures. The first one was given by Dana Williams (Dartmouth College), and served as an introduction to crossed products of C*-algebras and the study of their structure. The second series of lectures was delivered by Aidan Sims (Wollongong), who gave an overview of the theory of topological groupoids (as a model for groups and group actions) and groupoid C*-algebras, with particular emphasis on the case of étale groupoids. Finally, the last series was delivered by Gábor Szabó (Copenhagen), and consisted of an introduction to Rokhlin type properties (mostly centered around the work of Hirshberg, Winter and Zacharias) with hints to the more advanced theory related to groupoids.

Author : Jean Renault
Publisher : Springer
Page : 164 pages
File Size : 46,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540392187

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A Groupoid Approach to C*-Algebras by Jean Renault Pdf

Author : Goulnara Arzhantseva
Publisher : EPFL Press
Page : 312 pages
File Size : 44,5 Mb
Release : 2009-03-16
Category : Mathematics
ISBN : 1439804001

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Limits of Graphs in Group Theory and Computer Science by Goulnara Arzhantseva Pdf

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.

Author : Anatoly M. Vershik,Victor M. Buchstaber,Andrey V. Malyutin
Publisher : American Mathematical Soc.
Page : 345 pages
File Size : 51,7 Mb
Release : 2021-08-30
Category : Education
ISBN : 9781470456641

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Topology, Geometry, and Dynamics: V. A. Rokhlin-Memorial by Anatoly M. Vershik,Victor M. Buchstaber,Andrey V. Malyutin Pdf

Vladimir Abramovich Rokhlin (8/23/1919–12/03/1984) was one of the leading Russian mathematicians of the second part of the twentieth century. His main achievements were in algebraic topology, real algebraic geometry, and ergodic theory. The volume contains the proceedings of the Conference on Topology, Geometry, and Dynamics: V. A. Rokhlin-100, held from August 19–23, 2019, at The Euler International Mathematics Institute and the Steklov Institute of Mathematics, St. Petersburg, Russia. The articles deal with topology of manifolds, theory of cobordisms, knot theory, geometry of real algebraic manifolds and dynamical systems and related topics. The book also contains Rokhlin's biography supplemented with copies of actual very interesting documents.

Author : Ali Chamseddine,Caterina Consani,Nigel Higson,Masoud Khalkhali,Henri Moscovici,Guoliang Yu
Publisher : Springer Nature
Page : 753 pages
File Size : 41,9 Mb
Release : 2020-01-13
Category : Mathematics
ISBN : 9783030295974

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Advances in Noncommutative Geometry by Ali Chamseddine,Caterina Consani,Nigel Higson,Masoud Khalkhali,Henri Moscovici,Guoliang Yu Pdf

This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.

Author : V. Kaimanovich,A. Lodkin
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 44,7 Mb
Release : 2011-11-09
Category : Mathematics
ISBN : 9780821872895

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Representation Theory, Dynamical Systems, and Asymptotic Combinatorics by V. Kaimanovich,A. Lodkin Pdf

This volume, devoted to the 70th birthday of the well-known St. Petersburg mathematician A. M. Vershik, contains a collection of articles by participants in the conference "Representation Theory, Dynamical Systems, and Asymptotic Combinatorics", held in St. Petersburg in June of 2004. The book is suitable for graduate students and researchers interested in combinatorial and dynamical aspects of group representation theory.

Author : N.P. Landsman,Markus Pflaum,Martin Schlichenmaier
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 54,7 Mb
Release : 2001-10-01
Category : Mathematics
ISBN : 3764366087

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Quantization of Singular Symplectic Quotients by N.P. Landsman,Markus Pflaum,Martin Schlichenmaier Pdf

This is the first exposition of the quantization theory of singular symplectic (Marsden-Weinstein) quotients and their applications to physics. The reader will acquire an introduction to the various techniques used in this area, as well as an overview of the latest research approaches. These involve classical differential and algebraic geometry, as well as operator algebras and noncommutative geometry. Thus one will be amply prepared to follow future developments in this field.

Author : M. Amélia Bastos,Amarino Lebre,Stefan Samko,Ilya M. Spitkovsky
Publisher : Springer
Page : 373 pages
File Size : 42,5 Mb
Release : 2014-05-23
Category : Mathematics
ISBN : 9783034808163

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Operator Theory, Operator Algebras and Applications by M. Amélia Bastos,Amarino Lebre,Stefan Samko,Ilya M. Spitkovsky Pdf

This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i) operator theory and harmonic analysis (singular integral operators with shifts; pseudodifferential operators, factorization of almost periodic matrix functions; inequalities; Cauchy type integrals; maximal and singular operators on generalized Orlicz-Morrey spaces; the Riesz potential operator; modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras; inner endomorphisms of some semi group, crossed products; C*-algebras generated by mappings which have finite orbits; Folner sequences in operator algebras; arithmetic aspect of C*_r SL(2); C*-algebras of singular integral operators; algebras of operator sequences) and (iii) mathematical physics (operator approach to diffraction from polygonal-conical screens; Poisson geometry of difference Lax operators).

Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
Page : 568 pages
File Size : 48,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662104538

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Theory of Operator Algebras III by Masamichi Takesaki Pdf

From the reviews: "These three bulky volumes [EMS 124, 125, 127] [...] provide an introduction to this rapidly developing theory. [...] These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of mathematics. Furthermore, they should be on the bookshelf of every researcher of the area." Acta Scientiarum Mathematicarum