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The Geometry of the Word Problem for Finitely Generated Groups

Noel Brady, Tim Riley, Hamish Short (Autoren)

Buch | Softcover

IX, 206 Seiten

2006 | 2007
Springer Basel (Verlag)
978-3-7643-7949-0 (ISBN)

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lt;p>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.

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.

Erscheint lt. Verlag	12.12.2006
Reihe/Serie	Advanced Courses in Mathematics - CRM Barcelona
Zusatzinfo	IX, 206 p.
Verlagsort	Basel
Sprache	englisch
Maße	170 x 244 mm
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	Cayley graph • combinatorics • Dehn function • filling function • group theory • hyperbolic group • isoperimetric spectrum • Morse Theory • nilpotent group • Word problem
ISBN-10	3-7643-7949-9 / 3764379499
ISBN-13	978-3-7643-7949-0 / 9783764379490
Zustand	Neuware