The braided Ptolemy-Thompson group is finitely presented

Louis Funar (1) , Christophe Kapoudjian (2)

1 IF - Institut Fourier
2 IMT - Institut de Mathématiques de Toulouse UMR5219

Pursueing our investigations on the relations between Thompson groups and mapping class groups, we introduce the group $T^*$ (and its further generalizations) which is an extension of the Ptolemy-Thompson group $T$ by means of the full braid group $B_{\infty}$ on infinitely many strands. We prove that it is a finitely presented group with solvable word problem, and give an explicit presentation of it.

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

Louis Funar, Christophe Kapoudjian. The braided Ptolemy-Thompson group is finitely presented. Geometry and Topology, 2008, 12, pp.475-530. ⟨10.2140/gt.2008.12.475⟩. ⟨hal-00329844⟩