Continuous bounded cohomology of locally compact groups / Nicolas Monod.
By: Monod, NicolasMaterial type: TextSeries: Lecture notes in mathematics (Springer-Verlag): 1758.Publisher: Berlin ; New York : Springer, ©2001Description: 1 online resource (ix, 214 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783540449621; 3540449620Subject(s): Locally compact groups | Homology theory | Homology theory | Locally compact groupsGenre/Form: Electronic books. Additional physical formats: Print version:: Continuous bounded cohomology of locally compact groups.DDC classification: 510 s | 512/.55 LOC classification: QA3 | .L28 no. 1758 | QA387Online resources: Click here to access online
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Includes bibliographical references (pages 203-209) and index.
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.
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 Teichmller spaces. A special effort has been made to provide detailed proofs or references in quite some generality.