Continuous Bounded Cohomology of Locally Compact Groups

Nicolas Monod

ISBN 10: 3540420541 / ISBN 13: 9783540420545

Editore: Springer Berlin Heidelberg, Springer Berlin Heidelberg Jun 2001, 2001

Riguardo questo articolo

Neuware -Recent research has repeatedly led to connections between important rigidity questions and bounded cohomology. However, the latter has remained by and large intractable. This monograph introduces the functorial study of the continuous bounded cohomology for topological groups, with coefficients in Banach modules. The powerful techniques of this more general theory have successfully solved a number of the original problems in bounded cohomology. As applications, one obtains, in particular, rigidity results for actions on the circle, for representations on complex hyperbolic spaces and on Teichmüller spaces. A special effort has been made to provide detailed proofs or references in quite some generality.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 232 pp. Englisch.

Codice articolo 9783540420545

Dati bibliografici

• Titolo: Continuous Bounded Cohomology of Locally Compact Groups
• Editore: Springer Berlin Heidelberg, Springer Berlin Heidelberg Jun 2001
• Data di pubblicazione: 2001
• Lingua: Inglese
• ISBN 10: 3540420541
• ISBN 13: 9783540420545
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 229 L x 152 A x 13 P (millimetri) 229 millimetri di larghezza per 152 millimetri di altezza per 13 millimetri di profondità
• Peso: 343 grammi

Descrizione articolo

Riassunto

Recent research has repeatedly led to connections between important rigidity questions and bounded cohomology. However, the latter has remained by and large intractable. This monograph introduces the functorial study of the continuous bounded cohomology for topological groups, with coefficients in Banach modules. The powerful techniques of this more general theory have successfully solved a number of the original problems in bounded cohomology. As applications, one obtains, in particular, rigidity results for actions on the circle, for representations on complex hyperbolic spaces and on Teichmüller spaces. A special effort has been made to provide detailed proofs or references in quite some generality.

Contenuti

Introduction Chapter I Banach modules, $L^/infty$ spaces 1 Banach modules 2 $L^/infty$ spaces 3 Integration Chapter II Relative injectivity and amenable actions 4 Relative injectivity 5 Amenability and amenable actions Chapter III Definition and characterization of continuous bounded cohomology 6 A naive definition 7 The functorial characterization 8 Functoriality 9 Continuous cohomology and the comparison map Chapter IV Cohomological techniques 10 General techniques 11 Double ergodicity 12 Hochschild-Serre spectral sequence Chapter V Towards applications 13 Interpretations of $(^2 /rm EH)rm cb)$ 14 General irreducible lattices Bibliography Index