Bounded Cohomology Of Discrete Groups
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Bounded Cohomology Of Discrete Groups
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Author : Roberto Frigerio
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-11-21
Bounded Cohomology Of Discrete Groups written by Roberto Frigerio and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-21 with Algebra, Homological categories.
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.
Continuous Bounded Cohomology Of Locally Compact Groups
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Author : Nicolas Monod
language : en
Publisher: Springer
Release Date : 2003-07-01
Continuous Bounded Cohomology Of Locally Compact Groups written by Nicolas Monod and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Mathematics categories.
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.
Discrete Groups And Geometric Structures
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Author : Karel Dekimpe
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-11-12
Discrete Groups And Geometric Structures written by Karel Dekimpe and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-12 with Mathematics categories.
This volume reports on research related to Discrete Groups and Geometric Structures, as presented during the International Workshop held May 26-30, 2008, in Kortrijk, Belgium. Readers will benefit from impressive survey papers by John R. Parker on methods to construct and study lattices in complex hyperbolic space and by Ursula Hamenstadt on properties of group actions with a rank-one element on proper $\mathrm{CAT}(0)$-spaces. This volume also contains research papers in the area of group actions and geometric structures, including work on loops on a twice punctured torus, the simplicial volume of products and fiber bundles, the homology of Hantzsche-Wendt groups, rigidity of real Bott towers, circles in groups of smooth circle homeomorphisms, and groups generated by spine reflections admitting crooked fundamental domains.
Bounded Cohomology And Simplicial Volume
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Author : Caterina Campagnolo
language : en
Publisher: Cambridge University Press
Release Date : 2022-11-30
Bounded Cohomology And Simplicial Volume written by Caterina Campagnolo and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-30 with Mathematics categories.
An overview of bounded cohomology and simplicial volume covering the basics of the subject and recent research directions.
Combinatorial And Geometric Group Theory Edinburgh 1993
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Author : Andrew J. Duncan
language : en
Publisher: Cambridge University Press
Release Date : 1995
Combinatorial And Geometric Group Theory Edinburgh 1993 written by Andrew J. Duncan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
Authoritative collection of surveys and papers that will be indispensable to all research workers in the area.
Cohomology And K Theory Of Discrete Groups
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Author : Daniel Juan-Pineda
language : en
Publisher:
Release Date : 1994
Cohomology And K Theory Of Discrete Groups written by Daniel Juan-Pineda and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Cohomology In Banach Algebras
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Author : Barry Edward Johnson
language : en
Publisher: American Mathematical Soc.
Release Date : 1972
Cohomology In Banach Algebras written by Barry Edward Johnson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.
Let [Fraktur capital]A be a Banach algebra, [Fraktur capital]X a two-sided Banach [Fraktur capital] A-module, and define the cohomology groups [italic]H[italic superscript]n([Fraktur capital]A, [Fraktur capital]X) from the complex of bounded cochains in exact analogy to the classical (algebraic) case. This article gives an introduction to several aspects of the resulting theory.
Continuous Cohomology Discrete Subgroups And Representations Of Reductive Groups
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Author : Armand Borel
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-11-21
Continuous Cohomology Discrete Subgroups And Representations Of Reductive Groups written by Armand Borel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Mathematics categories.
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.
Geometry Topology And Dynamics In Negative Curvature
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Author : C. S. Aravinda
language : en
Publisher: Cambridge University Press
Release Date : 2016-01-21
Geometry Topology And Dynamics In Negative Curvature written by C. S. Aravinda and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-21 with Mathematics categories.
Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.
On The Algebraic Foundations Of Bounded Cohomology
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Author : Theo Bühler
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
On The Algebraic Foundations Of Bounded Cohomology written by Theo Bühler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
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.