The braided Ptolemy-Thompson group $T^{\ast }$ is asynchronously combable

Abstract

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

45p

References in corpus (2)

• The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V
• The Algebra of Strand Splitting. II. A Presentation for the Braid Group on One Strand