Introduction to the Baum-Connes Conjecture

By:

Alain Valette

Format:

Paperback / softback

Series:

Lectures in Mathematics. Eth Zurich

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Description

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.

Release date NZ

April 1st, 2002

Author

Alain Valette

Audiences

Postgraduate, Research & Scholarly
Professional & Vocational

Illustrations

X, 104 p.

Pages

104

Series

Lectures in Mathematics. Eth Zurich

Dimensions

170x244x6

ISBN-13

9783764367060

Product ID

5810999

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