Tame combings and almost convexity for groups
by
Susan Hermiller
New Mexico State University
Coauthors: John Meier

A tame combing for a finitely presented group is a 1-combing of the Cayley 2-complex associated to the presentation. In this talk we define a function that measures how tame such a 1-combing can be. The tameness functions associated to two different presentations of the same group are equivalent, in the sense that if one function is polynomial, then the other function is polynomial of the same degree, so this measurement is independent of the presentation chosen. By studying the tame combings associated to groups which admit a geodesic finite complete rewriting system, we have found a characterization of almost convexity for presentations of groups using the tameness function of the associated 1-combing.

Date received: April 13, 1998