Author: Michel Coornaert
Publisher:
ISBN:
Category :
Languages : en
Pages : 51

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Book Description

Author: Michel Coornaert
Publisher: Springer
ISBN: 3540475737
Category : Mathematics
Languages : en
Pages : 145

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Book Description
Gromov's theory of hyperbolic groups have had a big impact in combinatorial group theory and has deep connections with many branches of mathematics suchdifferential geometry, representation theory, ergodic theory and dynamical systems. This book is an elaboration on some ideas of Gromov on hyperbolic spaces and hyperbolic groups in relation with symbolic dynamics. Particular attention is paid to the dynamical system defined by the action of a hyperbolic group on its boundary. The boundary is most oftenchaotic both as a topological space and as a dynamical system, and a description of this boundary and the action is given in terms of subshifts of finite type. The book is self-contained and includes two introductory chapters, one on Gromov's hyperbolic geometry and the other one on symbolic dynamics. It is intended for students and researchers in geometry and in dynamical systems, and can be used asthe basis for a graduate course on these subjects.

Author: Michel Coornaert
Publisher:
ISBN: 9783662187852
Category :
Languages : en
Pages : 148

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Book Description

Author:
Publisher:
ISBN:
Category : Group actions (Mathematics)
Languages : en
Pages : 652

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Book Description
Publishes research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. Covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields.

Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 786

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Book Description

Author: Moʻatsah ha-leʼumit le-meḥḳar ule-fituaḥ (Israel)
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 850

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Book Description

Author: S.M. Gersten
Publisher: Springer Science & Business Media
ISBN: 1461395860
Category : Mathematics
Languages : en
Pages : 346

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Book Description
Essays in Group Theory contains five papers on topics of current interest which were presented in a seminar at MSRI, Berkeley in June, 1985. Special mention should be given to Gromov`s paper, one of the most significant in the field in the last decade. It develops the theory of hyperbolic groups to include a version of small cancellation theory sufficiently powerful to recover deep results of Ol'shanskii and Rips. Each of the remaining papers, by Baumslag and Shalen, Gersten, Shalen, and Stallings contains gems. For example, the reader will delight in Stallings' explicit construction of free actions of orientable surface groups on R-trees. Gersten's paper lays the foundations for a theory of equations over groups and contains a very quick solution to conjugacy problem for a class of hyperbolic groups. Shalen's article reviews the rapidly expanding theory of group actions on R-trees and the Baumslag-Shalen article uses modular representation theory to establish properties of presentations whose relators are pth-powers.

Author: F. Dahmani
Publisher: American Mathematical Soc.
ISBN: 1470421941
Category : Mathematics
Languages : en
Pages : 164

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Book Description
he authors introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a relatively hyperbolic group, while the latter one provides a natural framework for developing a geometric version of small cancellation theory. Examples of such families naturally occur in groups acting on hyperbolic spaces including hyperbolic and relatively hyperbolic groups, mapping class groups, , and the Cremona group. Other examples can be found among groups acting geometrically on spaces, fundamental groups of graphs of groups, etc. The authors obtain a number of general results about rotating families and hyperbolically embedded subgroups; although their technique applies to a wide class of groups, it is capable of producing new results even for well-studied particular classes. For instance, the authors solve two open problems about mapping class groups, and obtain some results which are new even for relatively hyperbolic groups.

Author: Alberto Verjovski
Publisher: #N/A
ISBN: 981456964X
Category :
Languages : en
Pages : 744

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Book Description
This proceedings presents the latest research materials done on group theory from geometrical viewpoint in particular Gromov's theory of hyperbolic groups, Coxeter groups, Tits buildings and actions on real trees. All these are very active subjects.

Author: Danny Calegari
Publisher: Mathematical Society Of Japan Memoirs
ISBN: 9784931469532
Category : Mathematics
Languages : en
Pages : 209

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Book Description
This book is a comprehensive introduction to the theory of stable commutator length, an important subfield of quantitative topology, with substantial connections to 2-manifolds, dynamics, geometric group theory, bounded cohomology, symplectic topology, and many other subjects. We use constructive methods whenever possible, and focus on fundamental and explicit examples. We give a self-contained presentation of several foundational results in the theory, including Bavard's Duality Theorem, the Spectral Gap Theorem, the Rationality Theorem, and the Central Limit Theorem. The contents should be accessible to any mathematician interested in these subjects, and are presented with a minimal number of prerequisites, but with a view to applications in many areas of mathematics.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets