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Record Nr. |
UNISA996466667703316 |
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Autore |
Monod Nicolas |
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Titolo |
Continuous Bounded Cohomology of Locally Compact Groups [[electronic resource] /] / by Nicolas Monod |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2001 |
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ISBN |
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Edizione |
[1st ed. 2001.] |
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Descrizione fisica |
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1 online resource (XII, 220 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1758 |
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Disciplina |
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Soggetti |
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Algebraic topology |
Topological groups |
Lie groups |
Group theory |
Algebraic Topology |
Topological Groups, Lie Groups |
Group Theory and Generalizations |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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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Sommario/riassunto |
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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 |
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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. |
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