Thomas Delzant's Books

A Universal Construction for Groups Acting Freely on Real Trees

By: Ian Chiswell,Thomas Müller

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A Universal Construction for Groups Acting Freely on Real Trees

By: Ian Chiswell,Thomas Müller

The theory of R-trees is a well-established and important area of geometric group theory and in this book the authors introduce a construction that provides a new perspective on group actions on R-trees. They construct a group RF(G), equipped with an action on an R-tree, whose elements are certain functions from a compact real interval to the group G. They also study the structure of RF(G), including a detailed description of centralizers of elements and an investigation of its subgroups and quotients. Any group acting freely on an R-tree embeds in RF(G) for some choice of G. Much remains to be done to understand RF(G), and the extensive list of open problems included in an appendix could potentially lead to new methods for investigating group actions on R-trees, particularly free actions. This book will interest all geometric group theorists and model theorists whose research involves R-trees.

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Page Count

300

Publisher

Cambridge University Press

Published Date

ISBN 10

1139576992

ISBN 13

9781139576994

Structure and Regularity of Group Actions on One-Manifolds

By: Sang-hyun Kim,Thomas Koberda

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Structure and Regularity of Group Actions on One-Manifolds

By: Sang-hyun Kim,Thomas Koberda

This book presents the theory of optimal and critical regularities of groups of diffeomorphisms, from the classical work of Denjoy and Herman, up through recent advances. Beginning with an investigation of regularity phenomena for single diffeomorphisms, the book goes on to describes a circle of ideas surrounding Filipkiewicz's Theorem, which recovers the smooth structure of a manifold from its full diffeomorphism group. Topics covered include the simplicity of homeomorphism groups, differentiability of continuous Lie group actions, smooth conjugation of diffeomorphism groups, and the reconstruction of spaces from group actions. Various classical and modern tools are developed for controlling the dynamics of general finitely generated group actions on one-dimensional manifolds, subject to regularity bounds, including material on Thompson's group F, nilpotent groups, right-angled Artin groups, chain groups, finitely generated groups with prescribed critical regularities, and applications to foliation theory and the study of mapping class groups. The book will be of interest to researchers in geometric group theory.

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Page Count

323

Publisher

Springer Nature

Published Date

ISBN 10

3030890066

ISBN 13

9783030890063

European Writers

By: William Thomas Hobdell Jackson,George Stade

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European Writers

By: William Thomas Hobdell Jackson,George Stade

See preceding entries. Volume 14 is the comprehensive index to the exemplary reference series providing access to authors, themes, and titles in both original and native versions. This volume also features a bibliographical supplement, a list of contributors, and master lists of subjects arranged alphabetically, chronologically, and by language. Annotation copyrighted by Book News, Inc., Portland, OR

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Page Count

728

Publisher

Macmillan Reference USA

Published Date

ISBN 10

0684192217

ISBN 13

9780684192215

Geometrie et theorie des groupes

Les groupes hyperboliques de Gromov

By: Michel Coornaert,Thomas Delzant,Athanase Papadopoulos

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Geometrie et theorie des groupes

Les groupes hyperboliques de Gromov

By: Michel Coornaert,Thomas Delzant,Athanase Papadopoulos

The book is an introduction of Gromov's theory of hyperbolic spaces and hyperbolic groups. It contains complete proofs of some basic theorems which are due to Gromov, and emphasizes some important developments on isoperimetric inequalities, automatic groups, and the metric structure on the boundary of a hyperbolic space.

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Page Count

165

Publisher

Springer

Published Date

ISBN 10

3540529772

ISBN 13

9783540529774

Book's by Thomas Delzant

A Universal Construction for Groups Acting Freely on Real Trees

A Universal Construction for Groups Acting Freely on Real Trees

Structure and Regularity of Group Actions on One-Manifolds

Structure and Regularity of Group Actions on One-Manifolds

European Writers

European Writers

Geometrie et theorie des groupes

Geometrie et theorie des groupes

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