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:
    non sort: The
    title: Geometric Hopf Invariant and Surgery Theory
  name:
    name part: Crabb, Michael.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Ranicki, Andrew.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2017
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVI, 397 p. 1 illus. in color. online resource.
  abstract: Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new. .
  table of contents: 1 The difference construction -- 2 Umkehr maps and inner product spaces -- 3 Stable homotopy theory -- 4 Z_2-equivariant homotopy and bordism theory -- 5 The geometric Hopf invariant -- 6 The double point theorem -- 7 The -equivariant geometric Hopf invariant -- 8 Surgery obstruction theory -- A The homotopy Umkehr map -- B Notes on Z2-bordism -- C The geometric Hopf invariant and double points (2010) -- References -- Index.
  note: by Michael Crabb, Andrew Ranicki.
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic topology
  subject:
    topic: Manifolds (Mathematics)
  subject:
    topic: Complex manifolds
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic Topology
  subject:
    topic: Manifolds and Cell Complexes (incl. Diff.Topology)
  classification: QA612-612.8
  classification: 514.2
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Monographs in Mathematics
  identifier: 9783319713069
  identifier: http://dx.doi.org/10.1007/978-3-319-71306-9
  record info:
    record creation date: 180125
    record change date: 20180125214503.0
    record identifier: 978-3-319-71306-9