Introduction To The Baum Connes Conjecture
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Introduction To The Baum Connes Conjecture
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Author : Alain Valette
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Introduction To The Baum Connes Conjecture written by Alain Valette 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.
The Baum-Connes conjecture is part of A. Connes' non-commutative geometry programme. It can be viewed as a conjectural generalisation of the Atiyah-Singer index theorem, to the equivariant setting (the ambient manifold is not compact, but some compactness is restored by means of a proper, co-compact action of a group "gamma"). Like the Atiyah-Singer theorem, the Baum-Connes conjecture states that a purely topological object coincides with a purely analytical one. For a given group "gamma", the topological object is the equivariant K-homology of the classifying space for proper actions of "gamma", while the analytical object is the K-theory of the C*-algebra associated with "gamma" in its regular representation. The Baum-Connes conjecture implies several other classical conjectures, ranging from differential topology to pure algebra. It has also strong connections with geometric group theory, as the proof of the conjecture for a given group "gamma" usually depends heavily on geometric properties of "gamma". This book is intended for graduate students and researchers in geometry (commutative or not), group theory, algebraic topology, harmonic analysis, and operator algebras. It presents, for the first time in book form, an introduction to the Baum-Connes conjecture. It starts by defining carefully the objects in both sides of the conjecture, then the assembly map which connects them. Thereafter it illustrates the main tool to attack the conjecture (Kasparov's theory), and it concludes with a rough sketch of V. Lafforgue's proof of the conjecture for co-compact lattices in in Spn1, SL(3R), and SL(3C).
Proper Group Actions And The Baum Connes Conjecture
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Author : Guido Mislin
language : en
Publisher:
Release Date : 2003-07-23
Proper Group Actions And The Baum Connes Conjecture written by Guido Mislin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-23 with categories.
An Introduction To C Algebras And Noncommutative Geometry
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Author : Heath Emerson
language : en
Publisher: Springer Nature
Release Date : 2024-07-27
An Introduction To C Algebras And Noncommutative Geometry written by Heath Emerson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-27 with Mathematics categories.
This is the first textbook on C*-algebra theory with a view toward Noncommutative Geometry. Moreover, it fills a gap in the literature, providing a clear and accessible account of the geometric picture of K-theory and its relation to the C*-algebraic picture. The text can be used as the basis for a graduate level or a capstone course with the goal being to bring a relative novice up to speed on the basic ideas while offering a glimpse at some of the more advanced topics of the subject. Coverage includes C*-algebra theory, K-theory, K-homology, Index theory and Connes’ Noncommuntative Riemannian geometry. Aimed at graduate level students, the book is also a valuable resource for mathematicians who wish to deepen their understanding of noncommutative geometry and algebraic K-theory. A wide range of important examples are introduced at the beginning of the book. There are lots of excellent exercises and any student working through these will benefit significantly. Prerequisites include a basic knowledge of algebra, analysis, and a bit of functional analysis. As the book progresses, a little more mathematical maturity is required as the text discusses smooth manifolds, some differential geometry and elliptic operator theory, and K-theory. The text is largely self-contained though occasionally the reader may opt to consult more specialized material to further deepen their understanding of certain details.
K Theory For Group C Algebras And Semigroup C Algebras
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Author : Joachim Cuntz
language : en
Publisher: Birkhäuser
Release Date : 2017-10-24
K Theory For Group C Algebras And Semigroup C Algebras written by Joachim Cuntz and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-24 with Mathematics categories.
This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is available here for the first time in book form. The topics discussed are among the most classical and intensely studied C*-algebras. They are important for applications in fields as diverse as the theory of unitary group representations, index theory, the topology of manifolds or ergodic theory of group actions. Part of the most basic structural information for such a C*-algebra is contained in its K-theory. The determination of the K-groups of C*-algebras constructed from group or semigroup actions is a particularly challenging problem. Paul Baum and Alain Connes proposed a formula for the K-theory of the reduced crossed product for a group action that would permit, in principle, its computation. By work of many hands, the formula has by now been verified for very large classes of groups and this work has led to the development of a host of new techniques. An important ingredient is Kasparov's bivariant K-theory. More recently, also the C*-algebras generated by the regular representation of a semigroup as well as the crossed products for actions of semigroups by endomorphisms have been studied in more detail. Intriguing examples of actions of such semigroups come from ergodic theory as well as from algebraic number theory. The computation of the K-theory of the corresponding crossed products needs new techniques. In cases of interest the K-theory of the algebras reflects ergodic theoretic or number theoretic properties of the action.
C Algebras
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Author : Joachim Cuntz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
C Algebras written by Joachim Cuntz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book contains a collection of articles provided by the participants of the SFB-workshop on C*-algebras, March 8 - March 12, 1999 which was held at the Sonderforschungsbereich "Geometrische Strukturen in der reinen Mathematik" of the University of Münster, Germany. The aim of the workshop was to bring together leading experts in the theory of C* -algebras with promising young researchers in the field, and to provide a stimulating atmosphere for discussions and interactions between the participants. There were 19 one-hour lectures on various topics like - classification of nuclear C* -algebras, - general K-theory for C* -algebras, - exact C* -algebras and exact groups, - C*-algebras associated to (infinite) matrices and C*-correspondences, - noncommutative prob ability theory, - deformation quantization, - group C* -algebras and the Baum-Connes conjecture, giving a broad overview of the latest developments in the field, and serving as a basis for discussions. We, the organizers of the workshop, were greatly pleased with the excellence of the lectures and so were led to the idea of publishing the proceedings of the conference. There are basically two kinds of contributions. On one side there are several articles giving surveys and overviews on new developments and im portant results of the theory, on the other side one finds original articles with interesting new results.
The Ubiquitous Heat Kernel
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Author : Jay Jorgenson
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
The Ubiquitous Heat Kernel written by Jay Jorgenson 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 2006 with Mathematics categories.
The aim of this volume is to bring together research ideas from various fields of mathematics which utilize the heat kernel or heat kernel techniques in their research. The intention of this collection of papers is to broaden productive communication across mathematical sub-disciplines and to provide a vehicle which would allow experts in one field to initiate research with individuals in another field, as well as to give non-experts a resource which can facilitate expanding theirresearch and connecting with others.
Operator Algebras And Their Applications
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Author : Robert S. Doran
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-07-28
Operator Algebras And Their Applications written by Robert S. Doran 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 2016-07-28 with Mathematics categories.
his volume contains the proceedings of the AMS Special Session Operator Algebras and Their Applications: A Tribute to Richard V. Kadison, held from January 10–11, 2015, in San Antonio, Texas. Richard V. Kadison has been a towering figure in the study of operator algebras for more than 65 years. His research and leadership in the field have been fundamental in the development of the subject, and his influence continues to be felt though his work and the work of his many students, collaborators, and mentees. Among the topics addressed in this volume are the Kadison-Kaplanksy conjecture, classification of C∗-algebras, connections between operator spaces and parabolic induction, spectral flow, C∗-algebra actions, von Neumann algebras, and applications to mathematical physics.
Novikov Conjectures Index Theorems And Rigidity Proceedings Of A Conference Organized At The Mathematisches Forschungs Institut Oberwolfach September 6 10 1993 2
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Author : Steven C. Ferry
language : en
Publisher: Cambridge University Press
Release Date : 1995
Novikov Conjectures Index Theorems And Rigidity Proceedings Of A Conference Organized At The Mathematisches Forschungs Institut Oberwolfach September 6 10 1993 2 written by Steven C. Ferry 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 1995 with Index theorems categories.
European Congress Of Mathematics
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Author : Carles Casacuberta
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
European Congress Of Mathematics written by Carles Casacuberta 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.
This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.
Handbook Of Homotopy Theory
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Author : Haynes Miller
language : en
Publisher: CRC Press
Release Date : 2020-01-23
Handbook Of Homotopy Theory written by Haynes Miller and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-23 with Mathematics categories.
The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.