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.
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Graduate
Illustrationen
Maße
Höhe: 244 mm
Breite: 170 mm
Dicke: 13 mm
Gewicht
ISBN-13
978-3-7643-7949-0 (9783764379490)
DOI
10.1007/978-3-7643-7950-6
Schweitzer Klassifikation
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.
