Geometric group theory
 Responsibility
 Cornelia Druţu, Michael Kapovich ; with an appendix by Bogdan Nica.
 Publication
 [Providence, Rhode Island] : American Mathematical Society, [2018]
 Copyright notice
 ©2018
 Physical description
 xx, 819 pages : illustrations ; 27 cm.
 Series
 Colloquium publications (American Mathematical Society) ; v. 63.
Access
Available online
Science Library (Li and Ma)
Stacks
Call number  Status 

QA1 .A5225 V.63  Unknown 
More options
Creators/Contributors
 Author/Creator
 Druţu, Cornelia, 1967 author.
 Contributor
 Kapovich, Michael, 1963 author.
 Nica, Bogdan, 1977 writer of appendix.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 787811) and index.
 Contents

 Geometry and topology Metric spaces Differential geometry Hyperbolic space Groups and their actions Median spaces and spaces with measured walls Finitely generated and finitely presented groups Coarse geometry Coarse topology Ultralimits of metric spaces Gromovhyperbolic spaces and groups Lattices in Lie groups Solvable groups Geometric aspects of solvable groups The Tits alternative Gromov's theorem The BanachTarski paradox Amenability and paradoxical decomposition Ultralimits, fixed point properties, proper actions Stallings's theorem and accessibility Proof of Stallings's theorem using harmonic functions Quasiconformal mappings Groups quasiisometric to $\mathbb{H}^n$ Quasiisometries of nonuniform lattices in $\mathbb{H}^n$ A survey of quasiisometric rigidity Appendix: Three theorems on linear groups Bibliography Index.
 (source: Nielsen Book Data)9781470411046 20180604
 Publisher's Summary
 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.
(source: Nielsen Book Data)9781470411046 20180604
Subjects
 Subject
 Geometric group theory.
 Group theory.
 Geometric group theory.
 Group theory.
 Group theory and generalizations > Special aspects of infinite or finite groups > Geometric group theory.
 Group theory and generalizations > Special aspects of infinite or finite groups > Hyperbolic groups and nonpositively curved groups.
 Group theory and generalizations > Special aspects of infinite or finite groups > Asymptotic properties of groups.
 Group theory and generalizations > Special aspects of infinite or finite groups > Generators, relations, and presentations.
 Group theory and generalizations > Special aspects of infinite or finite groups > Solvable groups, supersolvable groups.
 Group theory and generalizations > Special aspects of infinite or finite groups > Nilpotent groups.
 Group theory and generalizations > Special aspects of infinite or finite groups > Fundamental groups and their automorphisms.
 Group theory and generalizations > Structure and classification of infinite or finite groups > Groups acting on trees.
 Group theory and generalizations > Structure and classification of infinite or finite groups > Residual properties and generalizations; residually finite groups.
 Manifolds and cell complexes > Lowdimensional topology > Topological methods in group theory.
Bibliographic information
 Publication date
 2018
 Copyright date
 2018
 Series
 American Mathematical Society colloquium publications ; volume 63
 ISBN
 9781470411046 hardcover alkaline paper
 1470411040 hardcover alkaline paper