A new construction of 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 analysed: in many cases the language of words in the combing is an indexed language.
Cite this article
Martin R. Bridson, Combings of groups and the grammar of reparameterization. Comment. Math. Helv. 78 (2003), no. 4, pp. 752–771DOI 10.1007/S00014-003-0776-7