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

Louis Funar; Christophe Kapoudjian

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

Louis Funar·Christophe Kapoudjian

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Abstract

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.

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Louis Funar, Christophe Kapoudjian. 2006-02-22. The braided Ptolemy-Thompson group $T^*$ is asynchronously combable. https://arxiv.org/abs/math/0602490

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