Geometry and Topology 12 (2008) 475–530

DOI: 10.2140/gt.2008.12.475

Abstract

Pursuing our investigations on the relations between Thompson groups and mapping class groups, we introduce the group T^♯ (and its companion T^*) which is an extension of the Ptolemy–Thompson group T by the braid group B_∞ on infinitely many strands. We prove that T^♯ is a finitely presented group by constructing a complex on which it acts cocompactly with finitely presented stabilizers, and derive from it an explicit presentation. The groups T^♯ and T^* are in the same relation with respect to each other as the braid groups B_n+1 and B_n, for infinitely many strands n. We show that both groups embed as groups of homeomorphisms of the circle and their word problem is solvable.

Keywords

braid groups, mapping class groups, infinite surface, Thompson group

Mathematical Subject Classification

Primary: 20F36, 57M07

Secondary: 20F05, 20F38, 57N05

References

Publication

Received: 26 June 2007
Accepted: 21 November 2007
Published: 12 March 2008
Proposed: Shigeyuki Morita
Seconded: Joan Birman, Jean-Pierre Otal

Authors