The braided Ptolemy-Thompson group $T^*$ is asynchronously combable

Louis Funar (1) , Christophe Kapoudjian

1 IF - Institut Fourier

The braided Ptolemy-Thompson group $T^*$ is an extension of the Thompson group $T$ by the full braid group $B_{\infty}$ 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 $T^*$ is finitely presented. Our main result here is that $T^*$ (and $T$) is asynchronously combable. The method of proof is inspired by Lee Mosher's proof of automaticity of mapping class groups.

Domaines: Topologie géométrique [math.GT]; Théorie des groupes [math.GR]

Louis Funar, Christophe Kapoudjian. The braided Ptolemy-Thompson group $T^*$ is asynchronously combable. 2006. ⟨hal-00329832⟩