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TitleContinuous Bounded Cohomology of Locally Compact Groups [electronic resource] / edited by Nicolas Monod
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2001
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Descript XII, 220 p. online resource


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 Teichmรผller spaces. A special effort has been made to provide detailed proofs or references in quite some generality


Introduction; Chapter I: Banach modules, $Linfty$ spaces: Banach modules -- $L̂/infty$ 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

Mathematics Group theory Topological groups Lie groups Algebraic topology Mathematics Algebraic Topology Topological Groups Lie Groups Group Theory and Generalizations


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