Groups, Geometry, and Dynamics
Full-Text PDF (220 KB) |
Table of Contents | GGD summary
Copies of one-ended groups in mapping class groups
François Dahmani (1) and Koji Fujiwara (2)
(1) Institut de Mathématiques de Toulouse, Université Paul Sabatier, 31062, TOULOUSE CEDEX 9, FRANCE(2) Graduate School of Information Sciences, Tohoku University, 980-8578, SENDAI, JAPAN
We establish that, given Σ a compact orientable surface and G a finitely presented one-ended group, the set of copies of G in the mapping class group MCG(Σ) consisting of only pseudo-Anosov elements except identity is finite up to conjugacy. This relies on a result of Bowditch on the same problem for images of surfaces groups. He asked us whether we could reduce the case of one-ended groups to his result; this is a positive answer. Our work involves analogues of Rips and Sela’s canonical cylinders in curve complexes and an argument of Delzant to bound the number of images of a group in a hyperbolic group.
Keywords: Mapping class groups, pseudo-Anosov diffeomorphisms, curve complex