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Geometric Group Theory Asymptotic Invariants Of Infinite Groups
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Book Synopsis Geometric Group Theory: Asymptotic invariants of infinite groups by : Graham A. Niblo
Download or read book Geometric Group Theory: Asymptotic invariants of infinite groups written by Graham A. Niblo and published by Cambridge University Press. This book was released on 1993 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: For anyone whose interest lies in the interplay between groups and geometry, these books should be of interest.
Book Synopsis Geometric Group Theory: Asymptotic invariants of infinite groups by : Graham A. Niblo
Download or read book Geometric Group Theory: Asymptotic invariants of infinite groups written by Graham A. Niblo and published by . This book was released on 1993 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Group Theory by : Cornelia Druţu
Download or read book Geometric Group Theory written by Cornelia Druţu and published by American Mathematical Soc.. This book was released on 2018-03-28 with total page 841 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometric Group Theory by : Mladen Bestvina
Download or read book Geometric Group Theory written by Mladen Bestvina and published by American Mathematical Soc.. This book was released on 2014-12-24 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topics in Geometric Group Theory by : Pierre de la Harpe
Download or read book Topics in Geometric Group Theory written by Pierre de la Harpe and published by University of Chicago Press. This book was released on 2000-10-15 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Combinatorial and Geometric Group Theory by : Sean Cleary
Download or read book Combinatorial and Geometric Group Theory written by Sean Cleary and published by American Mathematical Soc.. This book was released on 2002 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume grew out of two AMS conferences held at Columbia University (New York, NY) and the Stevens Institute of Technology (Hoboken, NJ) and presents articles on a wide variety of topics in group theory. Readers will find a variety of contributions, including a collection of over 170 open problems in combinatorial group theory, three excellent survey papers (on boundaries of hyperbolic groups, on fixed points of free group automorphisms, and on groups of automorphisms of compactRiemann surfaces), and several original research papers that represent the diversity of current trends in combinatorial and geometric group theory. The book is an excellent reference source for graduate students and research mathematicians interested in various aspects of group theory.
Book Synopsis Geometric Group Theory Down Under by : John Cossey
Download or read book Geometric Group Theory Down Under written by John Cossey and published by Walter de Gruyter. This book was released on 2011-05-02 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Book Synopsis Combinatorial and Geometric Group Theory, Edinburgh 1993 by : Andrew J. Duncan
Download or read book Combinatorial and Geometric Group Theory, Edinburgh 1993 written by Andrew J. Duncan and published by Cambridge University Press. This book was released on 1995 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authoritative collection of surveys and papers that will be indispensable to all research workers in the area.
Book Synopsis Geometric and Computational Perspectives on Infinite Groups by : Gilbert Baumslag
Download or read book Geometric and Computational Perspectives on Infinite Groups written by Gilbert Baumslag and published by American Mathematical Soc.. This book was released on with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of two workshops on computational aspects of geometric group theory.
Book Synopsis Combinatorial and Geometric Group Theory by : Oleg Bogopolski
Download or read book Combinatorial and Geometric Group Theory written by Oleg Bogopolski and published by Springer Science & Business Media. This book was released on 2011-01-28 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometric Methods in Group Theory by : José Burillo
Download or read book Geometric Methods in Group Theory written by José Burillo and published by American Mathematical Soc.. This book was released on 2005 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometric Group Theory: Volume 1 by : Graham A. Niblo
Download or read book Geometric Group Theory: Volume 1 written by Graham A. Niblo and published by Cambridge University Press. This book was released on 1993-07-30 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: For anyone whose interest lies in the interplay between groups and geometry, these books will be an essential addition to their library.
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.
Book Synopsis Crystallographic Groups and Their Generalizations by : Paul Igodt
Download or read book Crystallographic Groups and Their Generalizations written by Paul Igodt and published by American Mathematical Soc.. This book was released on 2000 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles written by the invited speakers and workshop participants from the conference on "Crystallographic Groups and Their Generalizations", held at Katholieke Universiteit Leuven, Kortrijk (Belgium). Presented are recent developments and open problems. Topics include the theory of affine structures and polynomial structures, affine Schottky groups and crooked tilings, theory and problems on the geometry of finitely generated solvable groups, flat Lorentz 3-manifolds and Fuchsian groups, filiform Lie algebras, hyperbolic automorphisms and Anosov diffeomorphisms on infra-nilmanifolds, localization theory of virtually nilpotent groups and aspherical spaces, projective varieties, and results on affine appartment systems. Participants delivered high-level research mathematics and a discussion was held forum for new researchers. The survey results and original papers contained in this volume offer a comprehensive view of current developments in the field.
Book Synopsis Office Hours with a Geometric Group Theorist by : Matt Clay
Download or read book Office Hours with a Geometric Group Theorist written by Matt Clay and published by Princeton University Press. This book was released on 2017-07-11 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Invitations to Geometry and Topology by : Martin R. Bridson
Download or read book Invitations to Geometry and Topology written by Martin R. Bridson and published by . This book was released on 2002 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an array of topics that introduce the reader to key ideas in active areas in geometry and topology. The material is presented in a way that both graduate students and researchers should find accessible and enticing. The topics covered range from Morse theory and complex geometry theory to geometric group theory, and are accompanied by exercises that are designed to deepen the reader's understanding and to guide them in exciting directions for future investigation.
Book Synopsis Topics in Groups and Geometry by : Tullio Ceccherini-Silberstein
Download or read book Topics in Groups and Geometry written by Tullio Ceccherini-Silberstein and published by Springer Nature. This book was released on 2022-01-01 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.
