The Geometry of the Word Problem for Finitely Generated Groups

by Noel Brady, Tim Riley, Hamish Short

Overview

The origins of the word problem are in group theory, decidability and complexity. But through the vision of M. Gromov and the language of filling functions, the topic now impacts the world of large-scale geometry. This book contains accounts of many recent developments in Geometric Group Theory and shows the interaction between the word problem and geometry continues to be a central theme. It contains many figures, numerous exercises and open questions.

Product Details

ISBN-13:	9783764379490
Publisher:	Birkhäuser Basel
Publication date:	01/22/2007
Series:	Advanced Courses in Mathematics - CRM Barcelona
Edition description:	2007
Pages:	206
Product dimensions:	6.69(w) x 9.61(h) x 0.02(d)

Table of Contents

Dehn Functions and Non-Positive Curvature.- The Isoperimetric Spectrum.- Dehn Functions of Subgroups of CAT(0) Groups.- Filling Functions.- Filling Functions.- Relationships Between Filling Functions.- Example: Nilpotent Groups.- Asymptotic Cones.- Diagrams and Groups.- Dehn’s Problems and Cayley Graphs.- Van Kampen Diagrams and Pictures.- Small Cancellation Conditions.- Isoperimetric Inequalities and Quasi-Isometries.- Free Nilpotent Groups.- Hyperbolic-by-free groups.