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Introduction to the Baum-Connes Conjecture [Paperback]

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Item description for Introduction to the Baum-Connes Conjecture by Alain Valette...

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).



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Item Specifications...


Pages   116
Est. Packaging Dimensions:   Length: 9.2" Width: 6.5" Height: 0.3"
Weight:   0.65 lbs.
Binding  Softcover
Release Date   Jun 10, 2002
Publisher   Birkhäuser Basel
ISBN  3764367067  
ISBN13  9783764367060  


Availability  79 units.
Availability accurate as of Jan 21, 2017 08:58.
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More About Alain Valette


Register your artisan biography and upload your photo! Alain Valette is Professor of Mathematics at the Universite de Neuchatel, Switzerland.

Alain Valette has an academic affiliation as follows - Universit?? de Neuchatel, Switzerland Universite de Neuchatel, Switzer.

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Product Categories

1Books > Subjects > Professional & Technical > Professional Science > Mathematics > Geometry & Topology > Algebraic Geometry
2Books > Subjects > Professional & Technical > Professional Science > Mathematics > Geometry & Topology > Differential Geometry
3Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Algebra > General
4Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Functional Analysis
5Books > Subjects > Science > General
6Books > Subjects > Science > Mathematics > General
7Books > Subjects > Science > Mathematics > Geometry & Topology > Algebraic Geometry
8Books > Subjects > Science > Mathematics > Geometry & Topology > Differential Geometry
9Books > Subjects > Science > Mathematics > Geometry & Topology > General Geometry
10Books > Subjects > Science > Mathematics > Pure Mathematics > Algebra > General
11Books > Subjects > Science > Mathematics > Pure Mathematics > Calculus
12Books > Subjects > Science > Mathematics > Pure Mathematics > Functional Analysis



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