Overview

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 G. 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 G, the topological object is the equivariant K-homology of the classifying space for proper actions of G, while the analytical object is the K-theory of the C*-algebra associated with G 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 G usually depends heavily on geometric properties of G.

Full Product Details

Author:   Alain Valette
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   2002 ed.
Dimensions:   Width: 17.00cm , Height: 0.60cm , Length: 24.40cm
Weight:   0.240kg
ISBN:  

9783764367060

ISBN 10:   3764367067
Pages:   104
Publication Date:   01 April 2002
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Idempotents in Group Algebras.- 2 The Baum-Connes Conjecture.- 3K-theory for (Group) C*-algebras.- 4 Classifying Spaces andK-homology.- 5 EquivariantKK-theory.- 6 The Analytical Assembly Map.- 7 Some Examples of the Assembly Map.- 8 Property (RD).- 9 The Dirac-dual Dirac Method.- 10 Lafforgue’sKKBan Theory.- G. Mislin: On the Classifying Space for Proper Actions.- A.1 The topologist’s model.- A.2 The analyst’s model.- A.4 Spectra.

Reviews

Overall, the book is a very valuable addition to the literature on the Baum-Connes conjecture. It is highly recommended reading for anyone interested in learning more about the conjecture, or who does research in areas related to it. Of course, the reader who wants to be an expert will eventually have to consult the original literature, but such is inevitable in a book of this size (around 100 pages) and not necessarily a bad thing. --Mathematical Reviews

Overall, the book is a very valuable addition to the literature on the Baum-Connes conjecture. It is highly recommended reading for anyone interested in learning more about the conjecture, or who does research in areas related to it. Of course, the reader who wants to be an expert will eventually have to consult the original literature, but such is inevitable in a book of this size (around 100 pages) and not necessarily a bad thing. <p>--Mathematical Reviews

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