Buch, Englisch, Band 1758, 220 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 343 g
Reihe: Lecture Notes in Mathematics
Buch, Englisch, Band 1758, 220 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 343 g
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-540-42054-5
Verlag: Springer Berlin Heidelberg
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Topologie Algebraische Topologie
- Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
- Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
- Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
- Mathematik | Informatik Mathematik Algebra Homologische Algebra
Weitere Infos & Material
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.
