Mathematics, Department of
Date of this Version
2000
Citation
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 353, Number 3, Pages 943{962
Abstract
A 1-combing for a finitely presented group consists of a continuous family of paths based at the identity and ending at points x in the 1-skeleton of the Cayley 2-complex associated to the presentation. We define two functions (radial and ball tameness functions) that measure how efficiently a 1-combing moves away from the identity. These functions are geometric in the sense that they are quasi-isometry invariants. We show that a group is almost convex if and only if the radial tameness function is bounded by the identity function; hence almost convex groups, as well as certain generalizations of almost convex groups, are contained in the quasi-isometry class of groups admitting linear radial tameness functions.
Comments
Copyright 2000 American Mathematical Society