Noel Brady, Tim Riley, Hamish Short

The Geometry of the Word Problem for Finitely Generated Groups (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Basel AG
• Seitenzahl: 206
• Erscheinungstermin: 11. Mai 2007
• Englisch
• ISBN-13: 9783764379506
• Artikelnr.: 44223135

Inhaltsangabe

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.