Topological And Asymptotic Aspects Of Group Theory

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Topological and Asymptotic Aspects of Group Theory

R. I. Grigorchuk
Topological and Asymptotic Aspects of Group Theory Book PDF

Author : R. I. Grigorchuk
Publisher : American Mathematical Soc.
Page : 248 pages
File Size : 48,7 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821837566

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Topological and Asymptotic Aspects of Group Theory by R. I. Grigorchuk Pdf

The articles in this volume are based on the talks given at two special sessions at the AMS Sectional meetings held in 2004. The articles cover various topological and asymptotic aspects of group theory, such as hyperbolic and relatively hyperbolic groups, asymptotic cones, Thompson's group, Nielsen fixed point theory, homology, groups acting on trees, groups generated by finite automata, iterated monodromy groups, random walks on finitely generated groups, heat kernels, and currents on free groups.

Topological Methods in Group Theory

Ross Geoghegan
Topological Methods in Group Theory Book PDF

Author : Ross Geoghegan
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 52,7 Mb
Release : 2007-12-27
Category : Mathematics
ISBN : 9780387746142

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Topological Methods in Group Theory by Ross Geoghegan Pdf

This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.

Groups and Topological Dynamics

Volodymyr Nekrashevych
Groups and Topological Dynamics Book PDF

Author : Volodymyr Nekrashevych
Publisher : Unknown
Page : 0 pages
File Size : 48,5 Mb
Release : 2022
Category : Finite groups
ISBN : 1470471191

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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.

Geometric Group Theory

Cornelia Druţu,Michael Kapovich
Geometric Group Theory Book PDF

Author : Cornelia Druţu,Michael Kapovich
Publisher : American Mathematical Soc.
Page : 819 pages
File Size : 48,8 Mb
Release : 2018-03-28
Category : Geometric group theory
ISBN : 9781470411046

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Geometric Group Theory by Cornelia Druţu,Michael Kapovich Pdf

The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians. It fills a big gap in the literature and will be used by researchers in geometric group theory and its applications.

Papers on Group Theory and Topology

Max Dehn
Papers on Group Theory and Topology Book PDF

Author : Max Dehn
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461246688

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Papers on Group Theory and Topology by Max Dehn Pdf

The work of Max Dehn (1878-1952) has been quietly influential in mathematics since the beginning of the 20th century. In 1900 he became the first to solve one of the famous Hilbert problems (the third, on the decomposition of polyhedra), in 1907 he collaborated with Heegaard to produce the first survey of topology, and in 1910 he began publishing his own investigations in topology and combinatorial group theory. His influence is apparent in the terms Dehn's algorithm, Dehn's lemma and Dehn surgery (and Dehnsche Gruppenbilder, generally known in English as Cayley diagrams), but direct access to his work has been difficult. No edition of his works has been produced, and some of his most important results were never published, at least not by him. The present volume is a modest attempt to bring Dehn's work to a wider audience, particularly topologists and group theorists curious about the origins of their subject and interested in mining the sources for new ideas. It consists of English translations of eight works : five of Dehn's major papers in topology and combinatorial group theory, and three unpublished works which illuminate the published papers and contain some results not available elsewhere. In addition, I have written a short introduction to each work, summarising its contents and trying to establish its place among related works of Dehn and others, and I have added an appendix on the Dehn-Nielsen theorem (often known simply as Nielsen's theorem) .

Topology and Geometric Group Theory

Michael W. Davis,James Fowler,Jean-François Lafont,Ian J. Leary
Topology and Geometric Group Theory Book PDF

Author : Michael W. Davis,James Fowler,Jean-François Lafont,Ian J. Leary
Publisher : Springer
Page : 174 pages
File Size : 40,6 Mb
Release : 2016-09-14
Category : Mathematics
ISBN : 9783319436746

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Topology and Geometric Group Theory by Michael W. Davis,James Fowler,Jean-François Lafont,Ian J. Leary Pdf

This book presents articles at the interface of two active areas of research: classical topology and the relatively new field of geometric group theory. It includes two long survey articles, one on proofs of the Farrell–Jones conjectures, and the other on ends of spaces and groups. In 2010–2011, Ohio State University (OSU) hosted a special year in topology and geometric group theory. Over the course of the year, there were seminars, workshops, short weekend conferences, and a major conference out of which this book resulted. Four other research articles complement these surveys, making this book ideal for graduate students and established mathematicians interested in entering this area of research.

Combinatorial and Geometric Group Theory

Oleg Bogopolski,Inna Bumagin,Olga Kharlampovich,Enric Ventura
Combinatorial and Geometric Group Theory Book PDF

Author : Oleg Bogopolski,Inna Bumagin,Olga Kharlampovich,Enric Ventura
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 43,6 Mb
Release : 2011-01-28
Category : Mathematics
ISBN : 9783764399115

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Combinatorial and Geometric Group Theory by Oleg Bogopolski,Inna Bumagin,Olga Kharlampovich,Enric Ventura Pdf

This volume assembles several research papers in all areas of geometric and combinatorial group theory originated in the recent conferences in Dortmund and Ottawa in 2007. It contains high quality refereed articles developing new aspects of these modern and active fields in mathematics. It is also appropriate to advanced students interested in recent results at a research level.

Group Theory, Combinatorics, and Computing

Robert Fitzgerald Morse, Daniela Nikolova-Popova,Sarah Witherspoon
Group Theory Combinatorics and Computing Book PDF

Author : Robert Fitzgerald Morse, Daniela Nikolova-Popova,Sarah Witherspoon
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 45,7 Mb
Release : 2014-02-13
Category : Mathematics
ISBN : 9780821894354

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Group Theory, Combinatorics, and Computing by Robert Fitzgerald Morse, Daniela Nikolova-Popova,Sarah Witherspoon Pdf

This volume contains the proceedings of the International Conference on Group Theory, Combinatorics and Computing held from October 3-8, 2012, in Boca Raton, Florida. The papers cover a number of areas in group theory and combinatorics. Topics include finite simple groups, groups acting on structured sets, varieties of algebras, classification of groups generated by 3-state automata over a 2-letter alphabet, new methods for construction of codes and designs, groups with constraints on the derived subgroups of its subgroups, graphs related to conjugacy classes in groups, and lexicographical configurations. Application of computer algebra programs is incorporated in several of the papers. This volume includes expository articles on finite coverings of loops, semigroups and groups, and on the application of algebraic structures in the theory of communications. This volume is a valuable resource for researchers and graduate students working in group theory and combinatorics. The articles provide excellent examples of the interplay between the two areas.

Ischia Group Theory 2004

Zvi Arad,Marcel Herzog
Ischia Group Theory 2004 Book PDF

Author : Zvi Arad,Marcel Herzog
Publisher : American Mathematical Soc.
Page : 294 pages
File Size : 45,8 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821837115

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Ischia Group Theory 2004 by Zvi Arad,Marcel Herzog Pdf

Experts in the theory of finite groups and in representation theory provide insight into various aspects of group theory, such as the classification of finite simple groups, character theory, groups with special properties, table algebras, etc. Information for our distributors include: This book is co-published with Bar-Ilan University (Ramat-Gan, Israel).

Geometric and Topological Methods for Quantum Field Theory

Sylvie Paycha,Bernardo Uribe
Geometric and Topological Methods for Quantum Field Theory Book PDF

Author : Sylvie Paycha,Bernardo Uribe
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 55,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821840627

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Geometric and Topological Methods for Quantum Field Theory by Sylvie Paycha,Bernardo Uribe Pdf

This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures): Anomalies and noncommutative geometry, Deformation quantisation and Poisson algebras, Topological quantum field theory and orbifolds. These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.

Groups and Topological Dynamics

Volodymyr Nekrashevych
Groups and Topological Dynamics Book PDF

Author : Volodymyr Nekrashevych
Publisher : American Mathematical Society
Page : 708 pages
File Size : 40,8 Mb
Release : 2022-10-07
Category : Mathematics
ISBN : 9781470463809

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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.

Topological Methods in Group Theory

N. Broaddus,M. Davis,J.-F. Lafont,I. J. Ortiz
Topological Methods in Group Theory Book PDF

Author : N. Broaddus,M. Davis,J.-F. Lafont,I. J. Ortiz
Publisher : Cambridge University Press
Page : 211 pages
File Size : 45,5 Mb
Release : 2018-09-06
Category : Mathematics
ISBN : 9781108437622

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Topological Methods in Group Theory by N. Broaddus,M. Davis,J.-F. Lafont,I. J. Ortiz Pdf

Details some of the most recent developments at the interface of topology and geometric group theory. Ideal for graduate students.

Expanding Thurston Maps

Mario Bonk,Daniel Meyer
Expanding Thurston Maps Book PDF

Author : Mario Bonk,Daniel Meyer
Publisher : American Mathematical Soc.
Page : 478 pages
File Size : 40,5 Mb
Release : 2017-11-28
Category : Algebraic topology
ISBN : 9780821875544

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Expanding Thurston Maps by Mario Bonk,Daniel Meyer Pdf

This monograph is devoted to the study of the dynamics of expanding Thurston maps under iteration. A Thurston map is a branched covering map on a two-dimensional topological sphere such that each critical point of the map has a finite orbit under iteration. It is called expanding if, roughly speaking, preimages of a fine open cover of the underlying sphere under iterates of the map become finer and finer as the order of the iterate increases. Every expanding Thurston map gives rise to a fractal space, called its visual sphere. Many dynamical properties of the map are encoded in the geometry of this visual sphere. For example, an expanding Thurston map is topologically conjugate to a rational map if and only if its visual sphere is quasisymmetrically equivalent to the Riemann sphere. This relation between dynamics and fractal geometry is the main focus for the investigations in this work. The book is an introduction to the subject. The prerequisites for the reader are modest and include some basic knowledge of complex analysis and topology. The book has an extensive appendix, where background material is reviewed such as orbifolds and branched covering maps.

Gromov-Witten Theory of Spin Curves and Orbifolds

Tyler Jamison Jarvis,Takashi Kimura,Arkady Vaintrob
Gromov Witten Theory of Spin Curves and Orbifolds Book PDF

Author : Tyler Jamison Jarvis,Takashi Kimura,Arkady Vaintrob
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 42,9 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821835340

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Gromov-Witten Theory of Spin Curves and Orbifolds by Tyler Jamison Jarvis,Takashi Kimura,Arkady Vaintrob Pdf

This volume is a collection of articles on orbifolds, algebraic curves with higher spin structures, and related invariants of Gromov-Witten type. Orbifold Gromov-Witten theory generalizes quantum cohomology for orbifolds, whereas spin cohomological field theory is based on the moduli spaces of higher spin curves and is related by Witten's conjecture to the Gelfand-Dickey integrable hierarchies. A common feature of these two very different looking theories is the central role played by orbicurves in both of them. Insights in one theory can often yield insights into the other. This book brings together for the first time papers related to both sides of this interaction. The articles in the collection cover diverse topics, such as geometry and topology of orbifolds, cohomological field theories, orbifold Gromov-Witten theory, $G$-Frobenius algebra and singularities, Frobenius manifolds and Givental's quantization formalism, moduli of higher spin curves and spin cohomological field theory.

Operator Theory, Operator Algebras, and Applications

Deguang Han,Palle E. T. Jørgensen,David R. Larson
Operator Theory Operator Algebras and Applications Book PDF

Author : Deguang Han,Palle E. T. Jørgensen,David R. Larson
Publisher : American Mathematical Soc.
Page : 440 pages
File Size : 43,7 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821839232

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Operator Theory, Operator Algebras, and Applications by Deguang Han,Palle E. T. Jørgensen,David R. Larson Pdf

This book offers a presentation of some new trends in operator theory and operator algebras, with a view to their applications. It consists of separate papers written by some of the leading practitioners in the field. The content is put together by the three editors in a way that should help students and working mathematicians in other parts of the mathematical sciences gain insight into an important part of modern mathematics and its applications. While different specialist authors are outlining new results in this book, the presentations have been made user friendly with the aid of tutorial material. In fact, each paper contains three things: a friendly introduction with motivation, tutorial material, and new research. The authors have strived to make their results relevant to the rest of mathematics. A list of topics discussed in the book includes wavelets, frames and their applications, quantum dynamics, multivariable operator theory, $C*$-algebras, and von Neumann algebras. Some longer papers present recent advances on particular, long-standing problems such as extensions and dilations, the Kadison-Singer conjecture, and diagonals of self-adjoint operators.