Bounded cohomology of discrete groups

著者

• Frigerio, Roberto

書誌事項

Bounded cohomology of discrete groups

Roberto Frigerio

（Mathematical surveys and monographs, v. 227）

American Mathematical Society, c2017

注記

Includes bibliographical references (p. 187-193) and index

内容説明・目次

内容説明

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.

目次

(Bounded) cohomology of groups (Bounded) cohomology of groups in low degree Amenability (Bounded) group cohomology via resolutions Bounded cohomology of topological spaces $\ell^1$-homology and duality Simplicial volume The proportionality principle Additivity of the simplicial volume Group actions on the circle The Euler class of sphere bundles Milnor-Wood inequalities and maximal representations The bounded Euler class in higher dimensions and the Chern conjecture Index List of symbols Bibliography

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詳細情報

• NII書誌ID(NCID): BB25022456
• ISBN:
  • 9781470441463
• LCCN: 2017023394
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: xvi, 193 p.
• 大きさ: 27 cm
• 分類:
  • LCC : QA612.3
  • DC23 : 512/.55
• 件名:
  • LCSH : Intersection homology theory
  • LCSH : Homology theory
  • LCSH : Algebra, Homological
• 親書誌ID:
  • BA00134419