Introduction to the Baum-Connes Conjecture

Introduction to the Baum-Connes Conjecture
Alain Valette, Alain Valette
Not in Library

My Reading Lists:

Create a new list

Check-In

×Close
Add an optional check-in date. Check-in dates are used to track yearly reading goals.
Today


Buy this book

Last edited by ImportBot
January 31, 2024 | History

Introduction to the Baum-Connes Conjecture

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).

Publish Date
Publisher
Island Press
Language
English

Buy this book

Previews available in: English

Edition Availability
Cover of: Introduction to the Baum-Connes Conjecture
Introduction to the Baum-Connes Conjecture
2012, Birkhauser Verlag
in English
Cover of: Introduction to the Baum-Connes Conjecture
Introduction to the Baum-Connes Conjecture
2002, Birkhäuser Boston
in English
Cover of: Introduction to the Baum-Connes conjecture
Introduction to the Baum-Connes conjecture
2002, Birkhäuser Verlag
in English
Cover of: Introduction to the Baum-Connes Conjecture
Introduction to the Baum-Connes Conjecture
2002, Island Press
in English

Add another edition?

Book Details


The Physical Object

Pagination
120
Weight
0.205

ID Numbers

Open Library
OL50689824M
ISBN 13
9783034881883

Source records

Better World Books record

Community Reviews (0)

Feedback?
No community reviews have been submitted for this work.

Lists

This work does not appear on any lists.

History

Download catalog record: RDF / JSON / OPDS | Wikipedia citation
January 31, 2024 Created by ImportBot Imported from Better World Books record