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Description - 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 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.

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Book Details

ISBN: 9783764367060
ISBN-10: 3764367067
Format: Paperback
(244mm x 170mm x mm)
Pages: 104
Imprint: Birkhauser Verlag AG
Publisher: Birkhauser Verlag AG
Publish Date: 1-Apr-2002
Country of Publication: Switzerland

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