Bounded Cohomology of Discrete Groups

Released on by Roberto Frigerio
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  • Bounded Cohomology of Discrete Groups Book Detail

  • Author : Roberto Frigerio
  • Release Date : 2017-11-21
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 213
  • ISBN 13 : 1470441462
  • File Size : 17,17 MB
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Bounded Cohomology of Discrete Groups by Roberto Frigerio PDF Summary

Book Description: 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, self-contained 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 low-dimensional 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.

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Bounded Cohomology of Discrete Groups

Bounded Cohomology of Discrete Groups

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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

Bounded Cohomology and Simplicial Volume

Bounded Cohomology and Simplicial Volume

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Since their introduction by Gromov in the 1980s, the study of bounded cohomology and simplicial volume has developed into an active field connected to geometry