Amenability Of Discrete Groups By Examples

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Amenability of Discrete Groups by Examples

Kate Juschenko
Amenability of Discrete Groups by Examples Book PDF

Author : Kate Juschenko
Publisher : American Mathematical Society
Page : 180 pages
File Size : 47,7 Mb
Release : 2022-06-30
Category : Mathematics
ISBN : 9781470470326

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Amenability of Discrete Groups by Examples by Kate Juschenko Pdf

The main topic of the book is amenable groups, i.e., groups on which there exist invariant finitely additive measures. It was discovered that the existence or non-existence of amenability is responsible for many interesting phenomena such as, e.g., the Banach-Tarski Paradox about breaking a sphere into two spheres of the same radius. Since then, amenability has been actively studied and a number of different approaches resulted in many examples of amenable and non-amenable groups. In the book, the author puts together main approaches to study amenability. A novel feature of the book is that the exposition of the material starts with examples which introduce a method rather than illustrating it. This allows the reader to quickly move on to meaningful material without learning and remembering a lot of additional definitions and preparatory results; those are presented after analyzing the main examples. The techniques that are used for proving amenability in this book are mainly a combination of analytic and probabilistic tools with geometric group theory.

Amenable Locally Compact Groups

Jean-Paul Pier
Amenable Locally Compact Groups Book PDF

Author : Jean-Paul Pier
Publisher : Wiley-Interscience
Page : 440 pages
File Size : 49,8 Mb
Release : 1984-09-20
Category : Mathematics
ISBN : UCAL:B4406834

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Amenable Locally Compact Groups by Jean-Paul Pier Pdf

Collects the most recent results scattered throughout the literature on the theory of amenable groups, presenting a detailed investigation of the major features. The first part of the book discusses the different types of amenability properties, with basic examples listed. The second part provides complementary information on various aspects of amenability and a look at future directions.

Handbook of Teichmüller Theory

Athanase Papadopoulos
Handbook of Teichm ller Theory Book PDF

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
Page : 888 pages
File Size : 52,5 Mb
Release : 2007
Category : Mathematics
ISBN : 3037190558

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Handbook of Teichmüller Theory by Athanase Papadopoulos Pdf

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.

Lectures on Amenability

Volker Runde
Lectures on Amenability Book PDF

Author : Volker Runde
Publisher : Springer
Page : 302 pages
File Size : 54,8 Mb
Release : 2004-10-14
Category : Mathematics
ISBN : 9783540455608

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Lectures on Amenability by Volker Runde Pdf

The notion of amenability has its origins in the beginnings of modern measure theory: Does a finitely additive set function exist which is invariant under a certain group action? Since the 1940s, amenability has become an important concept in abstract harmonic analysis (or rather, more generally, in the theory of semitopological semigroups). In 1972, B.E. Johnson showed that the amenability of a locally compact group G can be characterized in terms of the Hochschild cohomology of its group algebra L^1(G): this initiated the theory of amenable Banach algebras. Since then, amenability has penetrated other branches of mathematics, such as von Neumann algebras, operator spaces, and even differential geometry. Lectures on Amenability introduces second year graduate students to this fascinating area of modern mathematics and leads them to a level from where they can go on to read original papers on the subject. Numerous exercises are interspersed in the text.

Bounded Cohomology of Discrete Groups

Roberto Frigerio
Bounded Cohomology of Discrete Groups Book PDF

Author : Roberto Frigerio
Publisher : American Mathematical Soc.
Page : 193 pages
File Size : 53,7 Mb
Release : 2017-11-21
Category : Algebra, Homological
ISBN : 9781470441463

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Bounded Cohomology of Discrete Groups by Roberto Frigerio Pdf

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.

Groupoids in Analysis, Geometry, and Physics

Arlan Ramsay,Jean Renault
Groupoids in Analysis Geometry and Physics Book PDF

Author : Arlan Ramsay,Jean Renault
Publisher : American Mathematical Soc.
Page : 208 pages
File Size : 55,7 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821820421

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Groupoids in Analysis, Geometry, and Physics by Arlan Ramsay,Jean Renault Pdf

Groupoids often occur when there is symmetry of a nature not expressible in terms of groups. Other uses of groupoids can involve something of a dynamical nature. Indeed, some of the main examples come from group actions. It should also be noted that in many situations where groupoids have been used, the main emphasis has not been on symmetry or dynamics issues. While the implicit symmetry and dynamics are relevant, the groupoid records mostly the structure of the space of leaves and the holonomy. More generally, the use of groupoids is very much related to various notions of orbit equivalance. This book presents the proceedings from the Joint Summer Research Conference on ``Groupoids in Analysis, Geometry, and Physics'' held in Boulder, CO. The book begins with an introduction to ways in which groupoids allow a more comprehensive view of symmetry than is seen via groups. Topics range from foliations, pseudo-differential operators, $KK$-theory, amenability, Fell bundles, and index theory to quantization of Poisson manifolds. Readers will find examples of important tools for working with groupoids. This book is geared to students and researchers. It is intended to improve their understanding of groupoids and to encourage them to look further while learning about the tools used.

Amenability

Alan L. T. Paterson
Amenability Book PDF

Author : Alan L. T. Paterson
Publisher : American Mathematical Soc.
Page : 474 pages
File Size : 44,6 Mb
Release : 1988
Category : Mathematics
ISBN : 9780821809853

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Amenability by Alan L. T. Paterson Pdf

The subject of amenability has its roots in the work of Lebesgue at the turn of the century. In the 1940s, the subject began to shift from finitely additive measures to means. This shift is of fundamental importance, for it makes the substantial resources of functional analysis and abstract harmonic analysis available to the study of amenability. The ubiquity of amenability ideas and the depth of the mathematics involved points to the fundamental importance of the subject. This book presents a comprehensive and coherent account of amenability as it has been developed in the large and varied literature during this century. The book has a broad appeal, for it presents an account of the subject based on harmonic and functional analysis. In addition, the analytic techniques should be of considerable interest to analysts in all areas. In addition, the book contains applications of amenability to a number of areas: combinatorial group theory, semigroup theory, statistics, differential geometry, Lie groups, ergodic theory, cohomology, and operator algebras. The main objectives of the book are to provide an introduction to the subject as a whole and to go into many of its topics in some depth. The book begins with an informal, nontechnical account of amenability from its origins in the work of Lebesgue. The initial chapters establish the basic theory of amenability and provide a detailed treatment of invariant, finitely additive measures (i.e., invariant means) on locally compact groups. The author then discusses amenability for Lie groups, "almost invariant" properties of certain subsets of an amenable group, amenability and ergodic theorems, polynomial growth, and invariant mean cardinalities. Also included are detailed discussions of the two most important achievements in amenability in the 1980s: the solutions to von Neumann's conjecture and the Banach-Ruziewicz Problem. The main prerequisites for this book are a sound understanding of undergraduate-level mathematics and a knowledge of abstract harmonic analysis and functional analysis. The book is suitable for use in graduate courses, and the lists of problems in each chapter may be useful as student exercises.

Mexican Mathematicians in the World

Fernando Galaz-García,Cecilia González-Tokman,Juan Carlos Pardo Millán
Mexican Mathematicians in the World Book PDF

Author : Fernando Galaz-García,Cecilia González-Tokman,Juan Carlos Pardo Millán
Publisher : American Mathematical Society
Page : 319 pages
File Size : 51,9 Mb
Release : 2021-11-22
Category : Mathematics
ISBN : 9781470465360

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Mexican Mathematicians in the World by Fernando Galaz-García,Cecilia González-Tokman,Juan Carlos Pardo Millán Pdf

Articles in this volume are based on presentations given at the IV Meeting of Mexican Mathematicians Abroad (IV Reunión de Matemáticos Mexicanos en el Mundo), held from June 10–15, 2018, at Casa Matemática Oaxaca (CMO), Mexico. This meeting was the fourth in a series of ongoing biannual meetings bringing together Mexican mathematicians working abroad with their peers in Mexico. This book features surveys and research articles from five broad research areas: algebra, analysis, combinatorics, geometry, and topology. Their topics range from general relativity and mathematical physics to interactions between logic and ergodic theory. Several articles provide a panoramic view of the fields and problems on which the authors are currently working on, showcasing diverse research lines complementary to those currently pursued in Mexico. The research-oriented manuscripts provide either alternative approaches to well-known problems or new advances in active research fields.

Groups and Topological Dynamics

Volodymyr Nekrashevych
Groups and Topological Dynamics Book PDF

Author : Volodymyr Nekrashevych
Publisher : American Mathematical Society
Page : 708 pages
File Size : 50,7 Mb
Release : 2022-10-11
Category : Mathematics
ISBN : 9781470471200

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Groups and Topological Dynamics by Volodymyr Nekrashevych Pdf

This book is devoted to group-theoretic aspects of topological dynamics such as studying groups using their actions on topological spaces, using group theory to study symbolic dynamics, and other connections between group theory and dynamical systems. One of the main applications of this approach to group theory is the study of asymptotic properties of groups such as growth and amenability. The book presents recently developed techniques of studying groups of dynamical origin using the structure of their orbits and associated groupoids of germs, applications of the iterated monodromy groups to hyperbolic dynamical systems, topological full groups and their properties, amenable groups, groups of intermediate growth, and other topics. The book is suitable for graduate students and researchers interested in group theory, transformations defined by automata, topological and holomorphic dynamics, and theory of topological groupoids. Each chapter is supplemented by exercises of various levels of complexity.

Banach Algebras and the General Theory of *-Algebras: Volume 2, *-Algebras

Theodore W. Palmer
Banach Algebras and the General Theory of Algebras Volume 2 Algebras Book PDF

Author : Theodore W. Palmer
Publisher : Cambridge University Press
Page : 846 pages
File Size : 45,8 Mb
Release : 1994
Category : Mathematics
ISBN : 0521366380

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Banach Algebras and the General Theory of *-Algebras: Volume 2, *-Algebras by Theodore W. Palmer Pdf

This second of two volumes gives a modern exposition of the theory of Banach algebras.

Sequences, Groups, and Number Theory

Valérie Berthé,Michel Rigo
Sequences Groups and Number Theory Book PDF

Author : Valérie Berthé,Michel Rigo
Publisher : Birkhäuser
Page : 578 pages
File Size : 47,7 Mb
Release : 2018-04-09
Category : Mathematics
ISBN : 9783319691527

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Sequences, Groups, and Number Theory by Valérie Berthé,Michel Rigo Pdf

This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.

Amenable Banach Algebras

Volker Runde
Amenable Banach Algebras Book PDF

Author : Volker Runde
Publisher : Springer Nature
Page : 468 pages
File Size : 41,6 Mb
Release : 2020-03-03
Category : Mathematics
ISBN : 9781071603512

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Amenable Banach Algebras by Volker Runde Pdf

This volume provides readers with a detailed introduction to the amenability of Banach algebras and locally compact groups. By encompassing important foundational material, contemporary research, and recent advancements, this monograph offers a state-of-the-art reference. It will appeal to anyone interested in questions of amenability, including those familiar with the author’s previous volume Lectures on Amenability. Cornerstone topics are covered first: namely, the theory of amenability, its historical context, and key properties of amenable groups. This introduction leads to the amenability of Banach algebras, which is the main focus of the book. Dual Banach algebras are given an in-depth exploration, as are Banach spaces, Banach homological algebra, and more. By covering amenability’s many applications, the author offers a simultaneously expansive and detailed treatment. Additionally, there are numerous exercises and notes at the end of every chapter that further elaborate on the chapter’s contents. Because it covers both the basics and cutting edge research, Amenable Banach Algebras will be indispensable to both graduate students and researchers working in functional analysis, harmonic analysis, topological groups, and Banach algebras. Instructors seeking to design an advanced course around this subject will appreciate the student-friendly elements; a prerequisite of functional analysis, abstract harmonic analysis, and Banach algebra theory is assumed.

Groups and Model Theory

Olga Kharlampovich,Rizos Sklinos
Groups and Model Theory Book PDF

Author : Olga Kharlampovich,Rizos Sklinos
Publisher : Walter de Gruyter GmbH & Co KG
Page : 250 pages
File Size : 46,8 Mb
Release : 2021-05-10
Category : Mathematics
ISBN : 9783110719765

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Groups and Model Theory by Olga Kharlampovich,Rizos Sklinos Pdf

This monograph provides an overview of developments in group theory motivated by model theory by key international researchers in the field. Topics covered include: stable groups and generalizations, model theory of nonabelian free groups and of rigid solvable groups, pseudofinite groups, approximate groups, topological dynamics, groups interpreting the arithmetic. The book is intended for mathematicians and graduate students in group theory and model theory. The book follows the course of the GAGTA (Geometric and Asymptotic Group Theory with Applications) conference series. The first book, "Complexity and Randomness in Group Theory. GAGTA book 1," can be found here: http://www.degruyter.com/books/978-3-11-066491-1 .

Handbook of Dynamical Systems

B. Hasselblatt,A. Katok
Handbook of Dynamical Systems Book PDF

Author : B. Hasselblatt,A. Katok
Publisher : Elsevier
Page : 1232 pages
File Size : 49,9 Mb
Release : 2002-08-20
Category : Mathematics
ISBN : 9780080533445

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Handbook of Dynamical Systems by B. Hasselblatt,A. Katok Pdf

Volumes 1A and 1B. These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample cross-references between individual surveys. The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics. Volume 1B will appear 2005.

Elements of Topological Dynamics

J. de Vries
Elements of Topological Dynamics Book PDF

Author : J. de Vries
Publisher : Springer Science & Business Media
Page : 762 pages
File Size : 48,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401581714

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Elements of Topological Dynamics by J. de Vries Pdf

This book is designed as an introduction into what I call 'abstract' Topological Dynamics (TO): the study of topological transformation groups with respect to problems that can be traced back to the qualitative theory of differential equa is in the tradition of the books [GH] and [EW. The title tions. So this book (,Elements . . . ' rather than 'Introduction . . . ') does not mean that this book should be compared, either in scope or in (intended) impact, with the 'Ele ments' of Euclid or Bourbaki. Instead, it reflects the choice and organisation of the material in this book: elementary and basic (but sufficient to understand recent research papers in this field). There are still many challenging prob lems waiting for a solution, and especially among general topologists there is a growing interest in this direction. However, the technical inaccessability of many research papers makes it almost impossible for an outsider to under stand what is going on. To a large extent, this inaccessability is caused by the lack of a good and systematic exposition of the fundamental methods and techniques of abstract TO. This book is an attempt to fill this gap. The guiding principle for the organization of the material in this book has been the exposition of methods and techniques rather than a discussion of the leading problems and their solutions. though the latter are certainly not neglected: they are used as a motivation wherever possible.