rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Introduction to the Baum-Connes conjecture
  name:
    name part: Valette, Alain.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: sz
    date issued: 2002
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (x, 104 pages)
  abstract: 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).
  note: Alain Valette.
  note: Electronic resource.
  note: Includes bibliographical references (pages [95]-101) and index.
  subject:
    topic: Baum-Connes conjecture
  subject:
    topic: KK-theory
  subject:
    topic: Noncommutative differential geometry
  subject:
    topic: Baum-Connes conjecture
  subject:
    topic: KK-theory
  subject:
    topic: Noncommutative differential geometry
  classification: QA614 .V35 2002eb
  classification: 516.3/6
  related item:
    title info:
      title: Lectures in mathematics ETH Zürich
  identifier: 9783034881876 (electronic bk.)
  identifier: 3034881878 (electronic bk.)
  identifier: 9783764367060
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: E7B
    record creation date: 020314
    record change date: 20260420201213.4
    record identifier: in00003549592
    language of cataloging:
      language term: eng