Continuous Bounded Cohomology of Locally Compact Groups

• Main Author: Monod, Nicolas (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001.
• Edition: 1st ed. 2001.
• Series: Lecture Notes in Mathematics, 1758
• Subjects: Algebraic topology.; Topological groups.; Lie groups.; Group theory.; Algebraic Topology.; Topological Groups, Lie Groups.; Group Theory and Generalizations.

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 B...

Table of Contents:

• 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.