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The Geometry of the Word Problem for Finitely Generated Groups
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ISBN-13:
9783764379490
Veröffentl:
2006
Einband:
Paperback
Erscheinungsdatum:
12.12.2006
Seiten:
220
Autor:
Noel Brady
Gewicht:
389 g
Format:
244x170x13 mm
Serie:
Advanced Courses in Mathematics - CRM Barcelona
Sprache:
Englisch
Beschreibung:
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
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.
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.