Bounded cohomology of discrete groups
 Responsibility
 Roberto Frigerio.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2017]
 Physical description
 xvi, 193 pages : illustrations ; 27 cm.
 Series
 Mathematical surveys and monographs ; no. 227.
Access
Available online
Science Library (Li and Ma)
Stacks
Call number  Status 

QA3 .A4 V.227  Unknown 
More options
Creators/Contributors
 Author/Creator
 Frigerio, Roberto, author.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 (Bounded) cohomology of groups(Bounded) cohomology of groups in low degreeAmenability(Bounded) group cohomology via resolutionsBounded cohomology of topological spaces$\ell^1$homology and dualitySimplicial volumeThe proportionality principleAdditivity of the simplicial volumeGroup actions on the circleThe Euler class of sphere bundlesMilnorWood inequalities and maximal representationsThe bounded Euler class in higher dimensions and the Chern conjectureIndexList of symbolsBibliography.
 (source: Nielsen Book Data)9781470441463 20180205
 Publisher's Summary
 The theory of bounded cohomology, introduced by Gromov in the late 1980s, has had powerful applications in geometric group theory and the geometry and topology of manifolds, and has been the topic of active research continuing to this day. This monograph provides a unified, selfcontained introduction to the theory and its applications, making it accessible to a student who has completed a first course in algebraic topology and manifold theory. The book can be used as a source for research projects for master's students, as a thorough introduction to the field for graduate students, and as a valuable landmark text for researchers, providing both the details of the theory of bounded cohomology and links of the theory to other closely related areas.The first part of the book is devoted to settling the fundamental definitions of the theory, and to proving some of the (by now classical) results on lowdimensional bounded cohomology and on bounded cohomology of topological spaces. The second part describes applications of the theory to the study of the simplicial volume of manifolds, to the classification of circle actions, to the analysis of maximal representations of surface groups, and to the study of flat vector bundles with a particular emphasis on the possible use of bounded cohomology in relation with the Chern conjecture. Each chapter ends with a discussion of further reading that puts the presented results in a broader context.
(source: Nielsen Book Data)9781470441463 20180205
Subjects
 Subject
 Intersection homology theory.
 Homology theory.
 Algebra, Homological.
 Category theory; homological algebra  Homological algebra  Other (co)homology theories.
 Group theory and generalizations  Connections with homological algebra and category theory  Cohomology of groups.
 Algebraic topology  Homology and cohomology theories  Singular theory.
 Manifolds and cell complexes  Topological manifolds  Algebraic topology of manifolds.
 Dynamical systems and ergodic theory  Lowdimensional dynamical systems  Maps of the circle.
 Dynamical systems and ergodic theory  Smooth dynamical systems: general theory  Dynamics of group actions other than $.
 Differential geometry  Global differential geometry  Global geometric and topological methods ( x00C3; x00A1; la Gromov); differential geometric analysis on metric spaces.
 Manifolds and cell complexes  Lowdimensional topology  Topological methods in group theory.
 Manifolds and cell complexes  Differential topology  Characteristic classes and numbers.
 Algebra, Homological.
 Homology theory.
 Intersection homology theory.
Bibliographic information
 Publication date
 2017
 Series
 Mathematical surveys and monographs ; volume 227
 ISBN
 9781470441463 hardcover
 1470441462 hardcover