The braided Ptolemy–Thompson group is an extension of the Thompson group by the full braid group on infinitely many strands and both of them can be viewed as mapping class groups of certain infinite planar surfaces. The main result of this article is that (and in particular ) is asynchronously combable. The result is new already for the group . The method of proof is inspired by Lee Mosher’s proof of automaticity of mapping class groups.
Cite this article
Louis Funar, Christophe Kapoudjian, The braided Ptolemy–Thompson group is asynchronously combable. Comment. Math. Helv. 86 (2011), no. 3, pp. 707–768DOI 10.4171/CMH/239