The Geometry of the Word Problem for Finitely Generated Groups

Noel Brady

ISBN 10: 3764379499 / ISBN 13: 9783764379490

Editore: Birkhäuser Basel, Springer Basel Dez 2006, 2006

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Neuware -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. Codice articolo 9783764379490

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Titolo: The Geometry of the Word Problem for ...

Casa editrice: Birkhäuser Basel, Springer Basel Dez 2006

Data di pubblicazione: 2006

Legatura: Taschenbuch

Condizione: Neu

Descrizione articolo

Riassunto:

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.

Contenuti:

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.