Continuous Bounded Cohomology And Applications To Rigidity Theory

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Continuous Bounded Cohomology of Locally Compact Groups

Author : Nicolas Monod
Publisher : Springer
ISBN 13 : 3540449620
Total Pages : 219 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Continuous Bounded Cohomology of Locally Compact Groups by : Nicolas Monod

Download or read book Continuous Bounded Cohomology of Locally Compact Groups written by Nicolas Monod and published by Springer. This book was released on 2003-07-01 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Gromov’s Theory of Multicomplexes with Applications to Bounded Cohomology and Simplicial Volume

Author : Roberto Frigerio
Publisher : American Mathematical Society
ISBN 13 : 1470459914
Total Pages : 166 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Gromov’s Theory of Multicomplexes with Applications to Bounded Cohomology and Simplicial Volume by : Roberto Frigerio

Download or read book Gromov’s Theory of Multicomplexes with Applications to Bounded Cohomology and Simplicial Volume written by Roberto Frigerio and published by American Mathematical Society. This book was released on 2023-03-09 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

On the Algebraic Foundations of Bounded Cohomology

Author : Theo Bühler
Publisher : American Mathematical Soc.
ISBN 13 : 0821853112
Total Pages : 126 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis On the Algebraic Foundations of Bounded Cohomology by : Theo Bühler

Download or read book On the Algebraic Foundations of Bounded Cohomology written by Theo Bühler and published by American Mathematical Soc.. This book was released on 2011 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Bounded Cohomology and Simplicial Volume

Author : Caterina Campagnolo
Publisher : Cambridge University Press
ISBN 13 : 100918329X
Total Pages : 171 pages
Book Rating : 4.0/5 (91 download)

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Book Synopsis Bounded Cohomology and Simplicial Volume by : Caterina Campagnolo

Download or read book Bounded Cohomology and Simplicial Volume written by Caterina Campagnolo and published by Cambridge University Press. This book was released on 2022-11-30 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of bounded cohomology and simplicial volume covering the basics of the subject and recent research directions.

Normed Amenability and Bounded Cohomology over Non-Archimedean Fields

Author : Francesco Fournier-Facio
Publisher : American Mathematical Society
ISBN 13 : 1470470918
Total Pages : 116 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Normed Amenability and Bounded Cohomology over Non-Archimedean Fields by : Francesco Fournier-Facio

Download or read book Normed Amenability and Bounded Cohomology over Non-Archimedean Fields written by Francesco Fournier-Facio and published by American Mathematical Society. This book was released on 2024-08-19 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Geometry, Rigidity, and Group Actions

Author : Benson Farb
Publisher : University of Chicago Press
ISBN 13 : 0226237907
Total Pages : 659 pages
Book Rating : 4.2/5 (262 download)

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Book Synopsis Geometry, Rigidity, and Group Actions by : Benson Farb

Download or read book Geometry, Rigidity, and Group Actions written by Benson Farb and published by University of Chicago Press. This book was released on 2011-04-15 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of group actions is more than a hundred years old but remains to this day a vibrant and widely studied topic in a variety of mathematic fields. A central development in the last fifty years is the phenomenon of rigidity, whereby one can classify actions of certain groups, such as lattices in semi-simple Lie groups. This provides a way to classify all possible symmetries of important spaces and all spaces admitting given symmetries. Paradigmatic results can be found in the seminal work of George Mostow, Gergory Margulis, and Robert J. Zimmer, among others. The papers in Geometry, Rigidity, and Group Actions explore the role of group actions and rigidity in several areas of mathematics, including ergodic theory, dynamics, geometry, topology, and the algebraic properties of representation varieties. In some cases, the dynamics of the possible group actions are the principal focus of inquiry. In other cases, the dynamics of group actions are a tool for proving theorems about algebra, geometry, or topology. This volume contains surveys of some of the main directions in the field, as well as research articles on topics of current interest.

Rigidity in Dynamics and Geometry

Author : Marc Burger
Publisher : Springer Science & Business Media
ISBN 13 : 3662047438
Total Pages : 494 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Rigidity in Dynamics and Geometry by : Marc Burger

Download or read book Rigidity in Dynamics and Geometry written by Marc Burger and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of proceedings is an offspring of the special semester Ergodic Theory, Geometric Rigidity and Number Theory which was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from Jan uary until July, 2000. Beside the activities during the semester, there were workshops held in January, March and July, the first being of introductory nature with five short courses delivered over a week. Although the quality of the workshops was excellent throughout the semester, the idea of these proceedings came about during the March workshop, which is hence more prominently represented, The format of the volume has undergone many changes, but what has remained untouched is the enthusiasm of the contributors since the onset of the project: suffice it to say that even though only two months elapsed between the time we contacted the potential authors and the deadline to submit the papers, the deadline was respected in the vast majority of the cases. The scope of the papers is not completely uniform throughout the volume, although there are some points in common. We asked the authors to write papers keeping in mind the idea that they should be accessible to students. At the same time, we wanted the papers not to be a summary of results that appeared somewhere else.

Random Walks and Geometry

Author : Vadim Kaimanovich
Publisher : Walter de Gruyter
ISBN 13 : 3110198088
Total Pages : 545 pages
Book Rating : 4.1/5 (11 download)

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Book Synopsis Random Walks and Geometry by : Vadim Kaimanovich

Download or read book Random Walks and Geometry written by Vadim Kaimanovich and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Die jüngsten Entwicklungen zeigen, dass sich Wahrscheinlichkeitsverfahren zu einem sehr wirkungsvollen Werkzeug entwickelt haben, und das auf so unterschiedlichen Gebieten wie statistische Physik, dynamische Systeme, Riemann'sche Geometrie, Gruppentheorie, harmonische Analyse, Graphentheorie und Informatik.

L2-Invariants: Theory and Applications to Geometry and K-Theory

Author : Wolfgang Lück
Publisher : Springer Science & Business Media
ISBN 13 : 3662046873
Total Pages : 604 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis L2-Invariants: Theory and Applications to Geometry and K-Theory by : Wolfgang Lück

Download or read book L2-Invariants: Theory and Applications to Geometry and K-Theory written by Wolfgang Lück and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.

Bounded Cohomology of Discrete Groups

Author : Roberto Frigerio
Publisher : American Mathematical Soc.
ISBN 13 : 1470441462
Total Pages : 213 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Bounded Cohomology of Discrete Groups by : Roberto Frigerio

Download or read book Bounded Cohomology of Discrete Groups written by Roberto Frigerio and published by American Mathematical Soc.. This book was released on 2017-11-21 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Limits of Graphs in Group Theory and Computer Science

Author : Goulnara Arzhantseva
Publisher : EPFL Press
ISBN 13 : 9781439804001
Total Pages : 312 pages
Book Rating : 4.8/5 (4 download)

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Book Synopsis Limits of Graphs in Group Theory and Computer Science by : Goulnara Arzhantseva

Download or read book Limits of Graphs in Group Theory and Computer Science written by Goulnara Arzhantseva and published by EPFL Press. This book was released on 2009-03-16 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of research articles and survey papers, this text highlights current methods and open problems in the geometric, combinatorial, and computational aspects of group theory. New interactions with broad areas of theoretical computer science are also considered. Pub 3/09.

Handbook of Teichmüller Theory

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
ISBN 13 : 9783037190555
Total Pages : 888 pages
Book Rating : 4.1/5 (95 download)

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Book Synopsis Handbook of Teichmüller Theory by : Athanase Papadopoulos

Download or read book Handbook of Teichmüller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.

Discrete Geometric Analysis

Author : Motoko Kotani
Publisher : American Mathematical Soc.
ISBN 13 : 0821833510
Total Pages : 274 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Discrete Geometric Analysis by : Motoko Kotani

Download or read book Discrete Geometric Analysis written by Motoko Kotani and published by American Mathematical Soc.. This book was released on 2004 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collects papers from the proceedings of the first symposium of the Japan Association for Mathematical Sciences. This book covers topics that center around problems of geometric analysis in relation to heat kernels, random walks, and Poisson boundaries on discrete groups, graphs, and other combinatorial objects.

Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology

Author : Paul Biran
Publisher : Springer Science & Business Media
ISBN 13 : 1402042663
Total Pages : 476 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology by : Paul Biran

Download or read book Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology written by Paul Biran and published by Springer Science & Business Media. This book was released on 2006-02-12 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers collected in this volume are contributions to the 43rd session of the Seminaire ́ de mathematiques ́ superieures ́ (SMS) on “Morse Theoretic Methods in Nonlinear Analysis and Symplectic Topology.” This session took place at the Universite ́ de Montreal ́ in July 2004 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together young researchers from various parts of the world and to present to them some of the most signi cant recent advances in these areas. More than 77 mathematicians from 17 countries followed the 12 series of lectures and participated in the lively exchange of ideas. The lectures covered an ample spectrum of subjects which are re ected in the present volume: Morse theory and related techniques in in nite dim- sional spaces, Floer theory and its recent extensions and generalizations, Morse and Floer theory in relation to string topology, generating functions, structure of the group of Hamiltonian di?eomorphisms and related dynamical problems, applications to robotics and many others. We thank all our main speakers for their stimulating lectures and all p- ticipants for creating a friendly atmosphere during the meeting. We also thank Ms. Diane Belanger ́ , our administrative assistant, for her help with the organi- tion and Mr. Andre ́ Montpetit, our technical editor, for his help in the preparation of the volume.

Geometric and Cohomological Methods in Group Theory

Author : Martin R. Bridson
Publisher : Cambridge University Press
ISBN 13 : 052175724X
Total Pages : 331 pages
Book Rating : 4.5/5 (217 download)

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Book Synopsis Geometric and Cohomological Methods in Group Theory by : Martin R. Bridson

Download or read book Geometric and Cohomological Methods in Group Theory written by Martin R. Bridson and published by Cambridge University Press. This book was released on 2009-10-29 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extended tour through a selection of the most important trends in modern geometric group theory.

Foliations and the Geometry of 3-Manifolds

Author : Danny Calegari
Publisher : Clarendon Press
ISBN 13 : 0191524638
Total Pages : 384 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Foliations and the Geometry of 3-Manifolds by : Danny Calegari

Download or read book Foliations and the Geometry of 3-Manifolds written by Danny Calegari and published by Clarendon Press. This book was released on 2007-05-17 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in 1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.

Group Actions in Ergodic Theory, Geometry, and Topology

Author : Robert J. Zimmer
Publisher : University of Chicago Press
ISBN 13 : 022656813X
Total Pages : 724 pages
Book Rating : 4.2/5 (265 download)

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Book Synopsis Group Actions in Ergodic Theory, Geometry, and Topology by : Robert J. Zimmer

Download or read book Group Actions in Ergodic Theory, Geometry, and Topology written by Robert J. Zimmer and published by University of Chicago Press. This book was released on 2019-12-23 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize his work over the course of his career. Zimmer’s body of work is remarkable in that it involves methods from a variety of mathematical disciplines, such as Lie theory, differential geometry, ergodic theory and dynamical systems, arithmetic groups, and topology, and at the same time offers a unifying perspective. After arriving at the University of Chicago in 1977, Zimmer extended his earlier research on ergodic group actions to prove his cocycle superrigidity theorem which proved to be a pivotal point in articulating and developing his program. Zimmer’s ideas opened the door to many others, and they continue to be actively employed in many domains related to group actions in ergodic theory, geometry, and topology. In addition to the selected papers themselves, this volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer recounting the course of his career in mathematics. The volume closes with an afterword by Fisher on the most recent developments around the Zimmer program.