Geometric Methods In Group Theory

Author : Clara Löh
Publisher : Springer
Page : 389 pages
File Size : 44,6 Mb
Release : 2017-12-19
Category : Mathematics
ISBN : 9783319722542

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Geometric Group Theory by Clara Löh Pdf

Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.

Author : Pierre de la Harpe
Publisher : University of Chicago Press
Page : 320 pages
File Size : 48,8 Mb
Release : 2000-10-15
Category : Education
ISBN : 0226317196

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Topics in Geometric Group Theory by Pierre de la Harpe Pdf

In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.

Author : Fedor Bogomolov,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 365 pages
File Size : 42,8 Mb
Release : 2006-06-22
Category : Mathematics
ISBN : 9780817644178

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Geometric Methods in Algebra and Number Theory by Fedor Bogomolov,Yuri Tschinkel Pdf

* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry

Author : AMS Special Session Geometric Group Theory
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 46,5 Mb
Release : 2005
Category : Finite groups
ISBN : 9780821833629

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Geometric Methods in Group Theory by AMS Special Session Geometric Group Theory Pdf

This volume presents articles by speakers and participants in two AMS special sessions, Geometric Group Theory and Geometric Methods in Group Theory, held respectively at Northeastern University (Boston, MA) and at Universidad de Sevilla (Spain). The expository and survey articles in the book cover a wide range of topics, making it suitable for researchers and graduate students interested in group theory.

Author : Vaughn Climenhaga,Anatole Katok
Publisher : American Mathematical Soc.
Page : 420 pages
File Size : 41,9 Mb
Release : 2017-04-07
Category : Geometry
ISBN : 9781470434793

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From Groups to Geometry and Back by Vaughn Climenhaga,Anatole Katok Pdf

Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth. The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness. This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009.

Author : Pierre de la Harpe
Publisher : University of Chicago Press
Page : 348 pages
File Size : 42,7 Mb
Release : 2000-09-15
Category : Mathematics
ISBN : 0226317218

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Topics in Geometric Group Theory by Pierre de la Harpe Pdf

In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.

Author : Goulnara N. Arzhantseva,Laurent Bartholdi,Jose Burillo,Enric Ventura
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 53,6 Mb
Release : 2007-09-24
Category : Mathematics
ISBN : 9783764384128

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Geometric Group Theory by Goulnara N. Arzhantseva,Laurent Bartholdi,Jose Burillo,Enric Ventura Pdf

This volume has its origins in the Barcelona Conference in Group Theory (July 2005) and the conference "Asymptotic and Probabilistic Methods in Geometric Group Theory" held in Geneva (June 2005). Twelve peer-reviewed research articles written by experts in the field present the most recent results in abstract and geometric group theory. In particular there are two articles by A. Juhász.

Author : Matt Clay,Dan Margalit
Publisher : Princeton University Press
Page : 456 pages
File Size : 50,5 Mb
Release : 2017-07-11
Category : Mathematics
ISBN : 9781400885398

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Office Hours with a Geometric Group Theorist by Matt Clay,Dan Margalit Pdf

Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincaré, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours with a Geometric Group Theorist brings together leading experts who provide one-on-one instruction on key topics in this exciting and relatively new field of mathematics. It's like having office hours with your most trusted math professors. An essential primer for undergraduates making the leap to graduate work, the book begins with free groups—actions of free groups on trees, algorithmic questions about free groups, the ping-pong lemma, and automorphisms of free groups. It goes on to cover several large-scale geometric invariants of groups, including quasi-isometry groups, Dehn functions, Gromov hyperbolicity, and asymptotic dimension. It also delves into important examples of groups, such as Coxeter groups, Thompson's groups, right-angled Artin groups, lamplighter groups, mapping class groups, and braid groups. The tone is conversational throughout, and the instruction is driven by examples. Accessible to students who have taken a first course in abstract algebra, Office Hours with a Geometric Group Theorist also features numerous exercises and in-depth projects designed to engage readers and provide jumping-off points for research projects.

Author : Ross Geoghegan
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 55,7 Mb
Release : 2007-12-17
Category : Mathematics
ISBN : 9780387746111

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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.

Author : Mladen Bestvina,Michah Sageev,Karen Vogtmann
Publisher : American Mathematical Soc.
Page : 417 pages
File Size : 45,9 Mb
Release : 2014-12-24
Category : Mathematics
ISBN : 9781470412272

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Geometric Group Theory by Mladen Bestvina,Michah Sageev,Karen Vogtmann Pdf

Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) groups. One course surveys quasi-isometric rigidity, others contain an exploration of the geometry of Outer space, of actions of arithmetic groups, lectures on lattices and locally symmetric spaces, on marked length spectra and on expander graphs, Property tau and approximate groups. This book is a valuable resource for graduate students and researchers interested in geometric group theory. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 48,9 Mb
Release : 2005
Category : Finite groups
ISBN : 0821833626

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Geometric Methods in Group Theory by Anonim Pdf

Author : Ross Geoghegan
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 41,9 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.

Author : Hamid Krim,A. Ben Hamza
Publisher : Cambridge University Press
Page : 299 pages
File Size : 40,8 Mb
Release : 2015-06-18
Category : Computers
ISBN : 9781107033900

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Geometric Methods in Signal and Image Analysis by Hamid Krim,A. Ben Hamza Pdf

A comprehensive guide to modern geometric methods for signal and image analysis, from basic principles to state-of-the-art concepts and applications.

Author : Roger C. Lyndon,Paul E. Schupp
Publisher : Springer
Page : 354 pages
File Size : 48,8 Mb
Release : 2015-03-12
Category : Mathematics
ISBN : 9783642618963

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Combinatorial Group Theory by Roger C. Lyndon,Paul E. Schupp Pdf

From the reviews: "This book [...] defines the boundaries of the subject now called combinatorial group theory. [...] it is a considerable achievement to have concentrated a survey of the subject into 339 pages. [...] a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews

Author : T. Mora,C. Traverso
Publisher : Springer Science & Business Media
Page : 504 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461204411

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Effective Methods in Algebraic Geometry by T. Mora,C. Traverso Pdf

The symposium "MEGA-90 - Effective Methods in Algebraic Geome try" was held in Castiglioncello (Livorno, Italy) in April 17-211990. The themes - we quote from the "Call for papers" - were the fol lowing: - Effective methods and complexity issues in commutative algebra, pro jective geometry, real geometry, algebraic number theory - Algebraic geometric methods in algebraic computing Contributions in related fields (computational aspects of group theory, differential algebra and geometry, algebraic and differential topology, etc.) were also welcome. The origin and the motivation of such a meeting, that is supposed to be the first of a series, deserves to be explained. The subject - the theory and the practice of computation in alge braic geometry and related domains from the mathematical viewpoin- has been one of the themes of the symposia organized by SIGSAM (the Special Interest Group for Symbolic and Algebraic Manipulation of the Association for Computing Machinery), SAME (Symbolic and Algebraic Manipulation in Europe), and AAECC (the semantics of the name is vary ing; an average meaning is "Applied Algebra and Error Correcting Codes").