The braided Ptolemy–Thompson group is asynchronously combable

  • Louis Funar

    Université Grenoble I, Saint-Martin-d'Hères, France
  • Christophe Kapoudjian

    Université Paul Sabatier – Toulouse 3, France


The braided Ptolemy–Thompson group TT^{\star} is an extension of the Thompson group TT by the full braid group BB_{\infty} 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 TT^{\star} (and in particular TT) is asynchronously combable. The result is new already for the group TT. 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. 707–768

DOI 10.4171/CMH/239