Bounded cohomology of discrete groups
著者
書誌事項
Bounded cohomology of discrete groups
（Mathematical surveys and monographs, v. 227）
American Mathematical Society, c2017
大学図書館所蔵 全31件
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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