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: Complex Kleinian Groups
  name:
    name part: Cano, Angel.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Navarrete, Juan Pablo.
    role:
      role term: author.
  name:
    name part: Seade, José.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XX, 272 p. online resource.
  abstract: This monograph lays down the foundations of the theory of complex Kleinian groups, a “newborn” area of mathematics whose origin can be traced back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can themselves be regarded as groups of holomorphic automorphisms of the complex projective line CP1. When we go into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere? or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories differ in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition; in the second, about an area of mathematics that is still in its infancy, and this is the focus of study in this monograph. It brings together several important areas of mathematics, e.g. classical Kleinian group actions, complex hyperbolic geometry, crystallographic groups and the uniformization problem for complex manifolds.
  table of contents: Preface -- Introduction -- Acknowledgments -- 1 A glance of the classical theory -- 2 Complex hyperbolic geometry -- 3 Complex Kleinian groups -- 4 Geometry and dynamics of automorphisms of P2C -- 5 Kleinian groups with a control group -- 6 The limit set in dimension two -- 7 On the dynamics of discrete subgroups of PU(n,1) -- 8 Projective orbifolds and dynamics in dimension two -- 9 Complex Schottky groups -- 10 Kleinian groups and twistor theory -- Bibliography -- Index. .
  note: by Angel Cano, Juan Pablo Navarrete, José Seade.
  subject:
    topic: Mathematics
  subject:
    topic: Topological groups
  subject:
    topic: Lie groups
  subject:
    topic: Dynamics
  subject:
    topic: Ergodic theory
  subject:
    topic: Functions of complex variables
  subject:
    topic: Mathematics
  subject:
    topic: Dynamical Systems and Ergodic Theory
  subject:
    topic: Topological Groups, Lie Groups
  subject:
    topic: Several Complex Variables and Analytic Spaces
  classification: QA313
  classification: 515.39
  classification: 515.48
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Progress in Mathematics ; 303
  identifier: 9783034804813
  identifier: http://dx.doi.org/10.1007/978-3-0348-0481-3
  record info:
    record creation date: 121116
    record change date: 20151204143412.0
    record identifier: 978-3-0348-0481-3