TY  - BOOK
AU  - Monod,Nicolas
ED  - SpringerLink (Online service)
TI  - Continuous Bounded Cohomology of Locally Compact Groups
T2  - Lecture Notes in Mathematics,
SN  - 9783540449621
AV  - QA612-612.8 
U1  - 514.2 23
PY  - 2001///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Group theory
KW  - Topological Groups
KW  - Algebraic topology
KW  - Algebraic Topology
KW  - Topological Groups, Lie Groups
KW  - Group Theory and Generalizations
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/b80626
ER  -