Abstract
Pursuing our investigations on the relations between Thompson groups and mapping class groups, we introduce the group (and its companion ) which is an extension of the Ptolemy–Thompson group by the braid group on infinitely many strands. We prove that 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 and are in the same relation with respect to each other as the braid groups and , for infinitely many strands . We show that both groups embed as groups of homeomorphisms of the circle and their word problem is solvable.
Citation
Louis Funar. Christophe Kapoudjian. "The braided Ptolemy–Thompson group is finitely presented." Geom. Topol. 12 (1) 475 - 530, 2008. https://doi.org/10.2140/gt.2008.12.475
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