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Author: Graham A. Niblo
Publisher: Cambridge University Press
Published: 1993
Total Pages: 307
ISBN-13: 0521446805
DOWNLOAD EBOOKFor anyone whose interest lies in the interplay between groups and geometry, these books should be of interest.
Author: Graham A. Niblo
Publisher:
Published: 1993
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: Cornelia DruĊ£u
Publisher: American Mathematical Soc.
Published: 2018-03-28
Total Pages: 841
ISBN-13: 1470411040
DOWNLOAD EBOOKThe 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.
Author: Mladen Bestvina
Publisher: American Mathematical Soc.
Published: 2014-12-24
Total Pages: 417
ISBN-13: 1470412276
DOWNLOAD EBOOKGeometric 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: Pierre de la Harpe
Publisher: University of Chicago Press
Published: 2000-10-15
Total Pages: 320
ISBN-13: 9780226317199
DOWNLOAD EBOOKIn 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: Sean Cleary
Publisher: American Mathematical Soc.
Published: 2002
Total Pages: 290
ISBN-13: 0821828223
DOWNLOAD EBOOKThis 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.
Author: John Cossey
Publisher: Walter de Gruyter
Published: 2011-05-02
Total Pages: 349
ISBN-13: 311080686X
DOWNLOAD EBOOKThe 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.
Author: Andrew J. Duncan
Publisher: Cambridge University Press
Published: 1995
Total Pages: 340
ISBN-13: 9780521465953
DOWNLOAD EBOOKAuthoritative collection of surveys and papers that will be indispensable to all research workers in the area.
Author: Gilbert Baumslag
Publisher: American Mathematical Soc.
Published:
Total Pages: 240
ISBN-13: 9780821870716
DOWNLOAD EBOOKThis book contains the proceedings of two workshops on computational aspects of geometric group theory.
Author: Oleg Bogopolski
Publisher: Springer Science & Business Media
Published: 2011-01-28
Total Pages: 318
ISBN-13: 3764399112
DOWNLOAD EBOOKThis 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.
