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Author: Roberto Frigerio
Publisher: American Mathematical Soc.
ISBN: 1470441462
Category : Mathematics
Languages : en
Pages : 213
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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.
Author: Roberto Frigerio
Publisher: American Mathematical Soc.
ISBN: 1470441462
Category : Mathematics
Languages : en
Pages : 213
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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.
Author: Nicolas Monod
Publisher: Springer
ISBN: 3540449620
Category : Mathematics
Languages : en
Pages : 219
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Book Description
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.
Author: Caterina Campagnolo
Publisher: Cambridge University Press
ISBN: 100918329X
Category : Mathematics
Languages : en
Pages : 171
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Book Description
An overview of bounded cohomology and simplicial volume covering the basics of the subject and recent research directions.
Author: Francesco Fournier-Facio
Publisher: American Mathematical Society
ISBN: 1470470918
Category : Mathematics
Languages : en
Pages : 116
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Book Description
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Author: Andrew J. Duncan
Publisher: Cambridge University Press
ISBN: 9780521465953
Category : Mathematics
Languages : en
Pages : 340
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Book Description
Authoritative collection of surveys and papers that will be indispensable to all research workers in the area.
Author: Armand Borel
Publisher: American Mathematical Soc.
ISBN: 147041225X
Category : Mathematics
Languages : en
Pages : 282
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Book Description
It has been nearly twenty years since the first edition of this work. In the intervening years, there has been immense progress in the use of homological algebra to construct admissible representations and in the study of arithmetic groups. This second edition is a corrected and expanded version of the original, which was an important catalyst in the expansion of the field. Besides the fundamental material on cohomology and discrete subgroups present in the first edition, this edition also contains expositions of some of the most important developments of the last two decades.
Author: Theo Bühler
Publisher: American Mathematical Soc.
ISBN: 0821853112
Category : Mathematics
Languages : en
Pages : 126
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Book Description
It is a widespread opinion among experts that (continuous) bounded cohomology cannot be interpreted as a derived functor and that triangulated methods break down. The author proves that this is wrong. He uses the formalism of exact categories and their derived categories in order to construct a classical derived functor on the category of Banach $G$-modules with values in Waelbroeck's abelian category. This gives us an axiomatic characterization of this theory for free, and it is a simple matter to reconstruct the classical semi-normed cohomology spaces out of Waelbroeck's category. The author proves that the derived categories of right bounded and of left bounded complexes of Banach $G$-modules are equivalent to the derived category of two abelian categories (one for each boundedness condition), a consequence of the theory of abstract truncation and hearts of $t$-structures. Moreover, he proves that the derived categories of Banach $G$-modules can be constructed as the homotopy categories of model structures on the categories of chain complexes of Banach $G$-modules, thus proving that the theory fits into yet another standard framework of homological and homotopical algebra.
Author: C. S. Aravinda
Publisher: Cambridge University Press
ISBN: 110752900X
Category : Mathematics
Languages : en
Pages : 378
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Book Description
Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.
Author: Roberto Frigerio
Publisher: American Mathematical Society
ISBN: 1470459914
Category : Mathematics
Languages : en
Pages : 166
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Book Description
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Author: Leonid A. Bokut'
Publisher: American Mathematical Soc.
ISBN: 0821851365
Category : Algebra
Languages : en
Pages : 742
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Book Description
