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: Homotopy Theory of C*-Algebras
  name:
    name part: Østvær, Paul Arne.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2010
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VI, 140p. online resource.
  abstract: Homotopy theory and C*-algebras are central topics in contemporary mathematics. This book introduces a modern homotopy theory for C*-algebras. One basic idea of the setup is to merge C*-algebras and spaces studied in algebraic topology into one category comprising C*-spaces. These objects are suitable fodder for standard homotopy theoretic moves, leading to unstable and stable model structures. With the foundations in place one is led to natural definitions of invariants for C*-spaces such as homology and cohomology theories, K-theory and zeta-functions. The text is largely self-contained. It serves a wide audience of graduate students and researchers interested in C*-algebras, homotopy theory and applications.
  table of contents: 1 Introduction -- 2 Preliminaries -- 2.1 C*-spaces -- 2.2 G – C*-spaces -- 2.3 Model categories -- 3 Unstable C*-homotopy theory -- 3.1 Pointwise model structures -- 3.2 Exact model structures -- 3.3 Matrix invariant model structures -- 3.4 Homotopy invariant model structures -- 3.5 Pointed model structures -- 3.6 Base change -- 4 Stable C*-homotopy theory -- 4.1 C*-spectra -- 4.2 Bispectra -- 4.3 Triangulated structure -- 4.4 Brown representability -- 4.5 C*-symmetric spectra -- 4.6 C*-functors -- 5 Invariants -- 5.1 Cohomology and homology theories -- 5.2 KK-theory and the Eilenberg-MacLane spectrum -- 5.3 HL-theory and the Eilenberg-MacLane -- 5.4 The Chern-Connes-Karoubi character -- 5.5 K-theory of C*-algebras -- 5.6 Zeta functions -- 6 The slice filtration -- References -- Index.
  note: by Paul Arne Østvær.
  subject:
    topic: Mathematics
  subject:
    topic: Functional analysis
  subject:
    topic: Algebraic topology
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic Topology
  subject:
    topic: Functional Analysis
  classification: QA612-612.8
  classification: 514.2
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Frontiers in Mathematics
  identifier: 9783034605656
  identifier: http://dx.doi.org/10.1007/978-3-0346-0565-6
  record info:
    record creation date: 100917
    record change date: 20130725201818.0
    record identifier: 978-3-0346-0565-6