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.
1
Université de Grenoble I, Saint-Martin-D'hères, France
2
Kyoto University, Japan
François Dahmani; Koji Fujiwara. Copies of one-ended groups in mapping class groups. Groups, geometry, and dynamics, Tome 3 (2009) no. 3, pp. 359-377. doi: 10.4171/ggd/61
@article{10_4171_ggd_61,
author = {Fran\c{c}ois Dahmani and Koji Fujiwara},
title = {Copies of one-ended groups in mapping class groups},
journal = {Groups, geometry, and dynamics},
pages = {359--377},
year = {2009},
volume = {3},
number = {3},
doi = {10.4171/ggd/61},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/61/}
}
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AU - François Dahmani
AU - Koji Fujiwara
TI - Copies of one-ended groups in mapping class groups
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