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Introduction to the Baum-Connes Conjecture
Paperback

Introduction to the Baum-Connes Conjecture

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This title is printed to order. This book may have been self-published. If so, we cannot guarantee the quality of the content. In the main most books will have gone through the editing process however some may not. We therefore suggest that you be aware of this before ordering this book. If in doubt check either the author or publisher’s details as we are unable to accept any returns unless they are faulty. Please contact us if you have any questions.

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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MORE INFO
Format
Paperback
Publisher
Birkhauser Verlag AG
Country
Switzerland
Date
1 April 2002
Pages
104
ISBN
9783764367060

This title is printed to order. This book may have been self-published. If so, we cannot guarantee the quality of the content. In the main most books will have gone through the editing process however some may not. We therefore suggest that you be aware of this before ordering this book. If in doubt check either the author or publisher’s details as we are unable to accept any returns unless they are faulty. Please contact us if you have any questions.

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.

Read More
Format
Paperback
Publisher
Birkhauser Verlag AG
Country
Switzerland
Date
1 April 2002
Pages
104
ISBN
9783764367060