The Geometry of the Word Problem for Finitely Generated Groups

• Main Authors: Brady, Noel (Author), Riley, Tim (Author), Short, Hamish (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2007.
• Series: Advanced Courses in Mathematics CRM Barcelona, Centre de Recerca Matemàtica
• Subjects: Mathematics.; Group theory.; Algebra.; Ordered algebraic structures.; Convex geometry.; Discrete geometry.; Combinatorics.; Group Theory and Generalizations.; Convex and Discrete Geometry.; Order, Lattices, Ordered Algebraic Structures.

Table of Contents:

• 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.