JournalscmhVol. 78 , No. 4DOI 10.1007/s00014-003-0776-7

Combings of groups and the grammar of reparameterization

  • Martin R. Bridson

    University of Oxford, UK
Combings of groups and the grammar of reparameterization cover

Abstract

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.