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: Geometric Group Theory
    sub title: An Introduction
  name:
    name part: Löh, Clara.
    role:
      role term: creator
    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: XI, 389 p. 119 illus., 100 illus. in color. online resource.
  abstract: Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.
  table of contents: 1 Introduction -- Part I Groups -- 2 Generating groups -- Part II Groups > Geometry -- 3 Cayley graphs -- 4 Group actions -- 5 Quasi-isometry -- Part III Geometry of groups -- 6 Growth types of groups -- 7 Hyperbolic groups -- 8 Ends and boundaries -- 9 Amenable groups -- Part IV Reference material -- A Appendix -- Bibliography -- Indices.
  note: by Clara Löh.
  subject:
    topic: Mathematics
  subject:
    topic: Group theory
  subject:
    topic: Differential geometry
  subject:
    topic: Hyperbolic geometry
  subject:
    topic: Manifolds (Mathematics)
  subject:
    topic: Complex manifolds
  subject:
    topic: Graph theory
  subject:
    topic: Mathematics
  subject:
    topic: Group Theory and Generalizations
  subject:
    topic: Differential Geometry
  subject:
    topic: Hyperbolic Geometry
  subject:
    topic: Manifolds and Cell Complexes (incl. Diff.Topology)
  subject:
    topic: Graph Theory
  classification: QA174-183
  classification: 512.2
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Universitext
  identifier: 9783319722542
  identifier: http://dx.doi.org/10.1007/978-3-319-72254-2
  record info:
    record creation date: 171220
    record change date: 20171220190023.0
    record identifier: 978-3-319-72254-2