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- catalog abstract "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.".
- catalog contributor b12157542.
- catalog created "2001.".
- catalog date "2001".
- catalog date "2001.".
- catalog dateCopyrighted "2001.".
- catalog description "Includes bibliographical references (p. [203]-209) and index.".
- catalog description "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.".
- catalog description "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.".
- catalog extent "ix, 214 p. :".
- catalog hasFormat "Also available in an electronic version.".
- catalog identifier "3540420541 (pbk. : alk. paper)".
- catalog isFormatOf "Also available in an electronic version.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1758.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1758".
- catalog issued "2001".
- catalog issued "2001.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer,".
- catalog relation "Also available in an electronic version.".
- catalog subject "510 s 512/.55 21".
- catalog subject "Algebraic topology.".
- catalog subject "Group theory.".
- catalog subject "Homology theory.".
- catalog subject "Locally compact groups.".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1758 QA387".
- catalog subject "Topological Groups.".
- catalog tableOfContents "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.".
- catalog title "Continuous bounded cohomology of locally compact groups / Nicolas Monod.".
- catalog type "Computer network resources. local".
- catalog type "Electronic books. lcsh".
- catalog type "text".