JSJ decompositions of groups / Vincent Guirardel, Gilbert Levitt.

Format:

Book

Author/Creator:

Guirardel, V. (Vincent), 1973- author.

Levitt, Gilbert, 1955- author.

Series:

Astérisque ; 395.

Astérisque, 0303-1179 ; 395

Language:

English

French

Subjects (All):

Group theory.

Cylindric algebras.

Amalgams (Group theory).

Physical Description:

vii, 165 pages : illustrations ; 24 cm.

Place of Publication:

Paris : Société Mathématique de France, 2017.

Language Note:

Text in English with abstracts in English and French.

Summary:

JSJ decompositions of finitely generated groups are a fundamental tool in geometric group theory, encoding all splittings of a group over a given class of subgroups. We give a unified account of this theory with complete proofs and many examples. We introduce a simple and general definition of JSJ decompositions, the natural object being a deformation space of actions on trees, similar to Outer Space. In many cases of interest, this deformation space contains a canonical JSJ tree, which is invariant under automorphisms.

Contents:

Introduction

Preliminaries

The JSJ deformation space

Flexible vertices

Acylindricity

Compatibility

R-trees, length functions, and compatibility.

Notes:

Includes bibliographical references (pages 157-162) and index.

ISBN:

9782856298701

2856298702

OCLC:

1022120150