30 research outputs found
A language theoretic analysis of combings
A group is combable if it can be represented by a language of words
satisfying a fellow traveller property; an automatic group has a synchronous
combing which is a regular language. This paper gives a systematic analysis of
the properties of groups with combings in various formal language classes, and
of the closure properties of the associated classes of groups. It generalises
previous work, in particular of Epstein et al. and Bridson and Gilman.Comment: DVI and Post-Script files only, 21 pages. Submitted to International
Journal of Algebra and Computatio
Hairdressing in groups: a survey of combings and formal languages
A group is combable if it can be represented by a language of words
satisfying a fellow traveller property; an automatic group has a synchronous
combing which is a regular language. This article surveys results for combable
groups, in particular in the case where the combing is a formal language.Comment: 17 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTMon1/paper24.abs.htm
The braided Ptolemy-Thompson group is asynchronously combable
The braided Ptolemy-Thompson group is an extension of the Thompson
group by the full braid group on infinitely many strands. This
group is a simplified version of the acyclic extension considered by Greenberg
and Sergiescu, and can be viewed as a mapping class group of a certain infinite
planar surface. In a previous paper we showed that is finitely presented.
Our main result here is that (and ) is asynchronously combable. The
method of proof is inspired by Lee Mosher's proof of automaticity of mapping
class groups.Comment: 45
Combable groups have group cohomology of polynomial growth
Group cohomology of polynomial growth is defined for any finitely generated
discrete group, using cochains that have polynomial growth with respect to the
word length function. We give a geometric condition that guarantees that it
agrees with the usual group cohomology and verify this condition for a class of
combable groups. Our condition involves a chain complex that is closely related
to exotic cohomology theories studied by Allcock and Gersten and by Mineyev.Comment: 19 pages, typo corrected in version