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Continuous Bounded Cohomology of Locally Compact Groups

Continuous Bounded Cohomology of Locally Compact Groups
Catalogue Information
Field name Details
Dewey Class 514.2
Title Continuous Bounded Cohomology of Locally Compact Groups ([EBook] /) / edited by Nicolas Monod.
Added Personal Name Monod, Nicolas editor.
Other name(s) SpringerLink (Online service)
Publication Berlin, Heidelberg : : Springer Berlin Heidelberg, , 2001.
Physical Details XII, 220 p. : online resource.
Series Lecture Notes in Mathematics 0075-8434 ; ; 1758
ISBN 9783540449621
Summary Note 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 Teichm├╝ller spaces. A special effort has been made to provide detailed proofs or references in quite some generality.:
Contents note Introduction; Chapter I: Banach modules, $Linfty$ spaces: Banach modules -- $L /infty$ spaces -- Integration. Chapter II: Relative injectivity and amenable actions: Relative injectivity -- Amenability and amenable actions. Chapter III: Definition and characterization of continuous bounded cohomology: A naive definition -- The functorial characterization -- Functoriality -- Continuous cohomology and the comparison map. Chapter IV: Cohomological techniques: General techniques -- Double ergodicity -- Hochschild-Serre spectral Sequence. Chapter V: Towards applications: Interpretations of $(/rm EH) 2 (/rm cb)$ -- General irreducible lattices. Bibliography. Index.
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