The Geometry of the Word Problem for Finitely Generated Groups
Published on 12. December 2006
Book
Paperback/Softback
IX, 206 pages
978-3-7643-7949-0 (ISBN)
Description
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.
More details
Series
Edition
2007 ed.
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Primary & secondary/elementary & high school
Graduate
Illustrations
IX, 206 p.
Dimensions
Height: 244 mm
Width: 170 mm
Thickness: 13 mm
Weight
389 gr
ISBN-13
978-3-7643-7949-0 (9783764379490)
DOI
10.1007/978-3-7643-7950-6
Schweitzer Classification
Other editions
Additional editions
Noel Brady | Tim Riley | Hamish Short
The Geometry of the Word Problem for Finitely Generated Groups
E-Book
05/2007
1st Edition
Birkhäuser
€29.99
Available for download
Content
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.