Combings of Groups and the Grammar of Reparameterization

Martin R. Bridson

Preprint 2000. To appear in Comm. Math. Helv.

A new method of constructing combings is used to distinguish between several previously indistinguishable classes of groups associated to the theory of automatic groups and non-positive curvature in group theory. We construct synchronously bounded combings for a class of groups that are neither bicombable nor automatic. The linguistic complexity of these combings is analyzed: in many cases the language of words in the combing is an indexed language.