Logo - springer
Slogan - springer

Birkhäuser - Birkhäuser Mathematics | Introduction to the Baum-Connes Conjecture

Introduction to the Baum-Connes Conjecture

Valette, Alain

2002, X, 104 p.

A product of Birkhäuser Basel
Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$19.99

(net) price for USA

ISBN 978-3-0348-8187-6

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase


learn more about Springer eBooks

add to marked items

Softcover
Information

Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$34.95

(net) price for USA

ISBN 978-3-7643-6706-0

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

A quick description of the conjecture The Baum-Connes conjecture is part of Alain Connes'tantalizing "noncommuta­ tive geometry" programme [18]. It is in some sense the most "commutative" part of this programme, since it bridges with classical geometry and topology. Let r be a countable group. The Baum-Connes conjecture identifies two objects associated with r, one analytical and one geometrical/topological. The right-hand side of the conjecture, or analytical side, involves the K­ theory of the reduced C*-algebra c;r, which is the C*-algebra generated by r in 2 its left regular representation on the Hilbert space C(r). The K-theory used here, Ki(C;r) for i = 0, 1, is the usual topological K-theory for Banach algebras, as described e.g. in [85]. The left-hand side of the conjecture, or geometrical/topological side RKf(Er) (i=O,I), is the r-equivariant K-homology with r-compact supports of the classifying space Er for proper actions of r. If r is torsion-free, this is the same as the K-homology (with compact supports) of the classifying space Br (or K(r,l) Eilenberg-Mac Lane space). This can be defined purely homotopically.

Content Level » Research

Keywords » Algebraic topology - K-theory - Non-commutative geometry - algebra - group algebras - group theory - homology

Related subjects » Birkhäuser Mathematics

Table of contents 

1 Idempotents in Group Algebras.- 2 The Baum-Connes Conjecture.- 3K-theory for (Group) C*-algebras.- 4 Classifying Spaces andK-homology.- 5 EquivariantKK-theory.- 6 The Analytical Assembly Map.- 7 Some Examples of the Assembly Map.- 8 Property (RD).- 9 The Dirac-dual Dirac Method.- 10 Lafforgue’sKKBan Theory.- G. Mislin: On the Classifying Space for Proper Actions.- A.1 The topologist’s model.- A.2 The analyst’s model.- A.4 Spectra.

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Algebra.