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Author : Martin R. Bridson
Publisher : Cambridge University Press
Page : 331 pages
File Size : 45,8 Mb
Release : 2009-10-29
Category : Mathematics
ISBN : 9780521757249
An extended tour through a selection of the most important trends in modern geometric group theory.
Author : Martin R. Bridson,Peter H. Kropholler,Ian J. Leary
Publisher : Unknown
Page : 331 pages
File Size : 41,5 Mb
Release : 2014-05-14
Category : Geometric group theory
ISBN : 113912742X
An extended tour through a selection of the most important trends in modern geometric group theory.
Author : Peter H. Kropholler,Ian J. Leary,Conchita Martínez-Pérez,Brita E. A. Nucinkis
Publisher : Cambridge University Press
Page : 277 pages
File Size : 46,7 Mb
Release : 2018
Category : Mathematics
ISBN : 9781316623220
Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.
Author : Ross Geoghegan
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 53,6 Mb
Release : 2007-12-27
Category : Mathematics
ISBN : 9780387746142
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 : Peter H. Kropholler,Graham A. Niblo,Ralph Stöhr
Publisher : Cambridge University Press
Page : 332 pages
File Size : 43,5 Mb
Release : 1998-05-14
Category : Mathematics
ISBN : 9780521635561
This volume reflects the fruitful connections between group theory and topology. It contains articles on cohomology, representation theory, geometric and combinatorial group theory. Some of the world's best known figures in this very active area of mathematics have made contributions, including substantial articles from Ol'shanskii, Mikhajlovskii, Carlson, Benson, Linnell, Wilson and Grigorchuk, which will be valuable reference works for some years to come. Pure mathematicians working in the fields of algebra, topology, and their interactions, will find this book of great interest.
Author : Clara Löh
Publisher : Springer
Page : 389 pages
File Size : 46,8 Mb
Release : 2017-12-19
Category : Mathematics
ISBN : 9783319722542
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 : Graham A. Niblo,Martin A. Roller
Publisher : Cambridge University Press
Page : 226 pages
File Size : 46,7 Mb
Release : 1993-07-30
Category : Mathematics
ISBN : 9780521435291
For anyone whose interest lies in the interplay between groups and geometry, these books will be an essential addition to their library.
Author : N. Broaddus,M. Davis,J.-F. Lafont,I. J. Ortiz
Publisher : Cambridge University Press
Page : 211 pages
File Size : 50,9 Mb
Release : 2018-09-06
Category : Mathematics
ISBN : 9781108437622
Details some of the most recent developments at the interface of topology and geometric group theory. Ideal for graduate students.
Author : D.J. Collins
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 54,6 Mb
Release : 1998-03-17
Category : Mathematics
ISBN : 3540637044
From the reviews: "... The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ..." Bulletin of the London Mathematical Society, 1996
Author : William Dwyer,Hans-Werner Henn
Publisher : Springer Science & Business Media
Page : 116 pages
File Size : 40,8 Mb
Release : 2001-10-01
Category : Mathematics
ISBN : 3764366052
This book consists essentially of notes which were written for an Advanced Course on Classifying Spaces and Cohomology of Groups. The course took place at the Centre de Recerca Mathematica (CRM) in Bellaterra from May 27 to June 2, 1998 and was part of an emphasis semester on Algebraic Topology. It consisted of two parallel series of 6 lectures of 90 minutes each and was intended as an introduction to new homotopy theoretic methods in group cohomology. The first part of the book is concerned with methods of decomposing the classifying space of a finite group into pieces made of classifying spaces of appropriate subgroups. Such decompositions have been used with great success in the last 10-15 years in the homotopy theory of classifying spaces of compact Lie groups and p-compact groups in the sense of Dwyer and Wilkerson. For simplicity the emphasis here is on finite groups and on homological properties of various decompositions known as centralizer resp. normalizer resp. subgroup decomposition. A unified treatment of the various decompositions is given and the relations between them are explored. This is preceeded by a detailed discussion of basic notions such as classifying spaces, simplicial complexes and homotopy colimits.
Author : C. Allday,V. Puppe
Publisher : Cambridge University Press
Page : 486 pages
File Size : 48,8 Mb
Release : 1993-07
Category : Mathematics
ISBN : 9780521350228
This is an account of the theory of certain types of compact transformation groups, namely those that are susceptible to study using ordinary cohomology theory and rational homotopy theory, which in practice means the torus groups and elementary abelian p-groups. The efforts of many mathematicians have combined to bring a depth of understanding to this area. However to make it reasonably accessible to a wide audience, the authors have streamlined the presentation, referring the reader to the literature for purely technical results and working in a simplified setting where possible. In this way the reader with a relatively modest background in algebraic topology and homology theory can penetrate rather deeply into the subject, whilst the book at the same time makes a useful reference for the more specialised reader.
Author : Mladen Bestvina,Michah Sageev,Karen Vogtmann
Publisher : American Mathematical Soc.
Page : 417 pages
File Size : 49,9 Mb
Release : 2014-12-24
Category : Mathematics
ISBN : 9781470412272
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 : Cornelia Druţu,Michael Kapovich
Publisher : American Mathematical Soc.
Page : 819 pages
File Size : 47,9 Mb
Release : 2018-03-28
Category : Geometric group theory
ISBN : 9781470411046
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.
Author : Wolfgang Metzler,Stephan Rosebrock
Publisher : Cambridge University Press
Page : 193 pages
File Size : 54,9 Mb
Release : 2018
Category : Mathematics
ISBN : 9781316600900
Presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Useful for both students and experts.
Author : K. W. Gruenberg
Publisher : Springer
Page : 293 pages
File Size : 42,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540363033
