Pseudo-Anosov subgroups of fibered 3-manifold groups
Spencer Dowdall
University of Illinois at Urbana-Champaign, USARichard P. Kent IV
University of Wisconsin, Madison, USAChristopher J. Leininger
University of Illinois at Urbana-Champaign, USA
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Abstract
Let be a hyperbolic surface and let be the surface obtained from by removing a point. The mapping class groups and fit into a short exact sequence
If is a hyperbolic -manifold that fibers over the circle with fiber , then its fundamental group fits into a short exact sequence
that injects into the one above. We show that, when viewed as subgroups of , finitely generated purely pseudo-Anosov subgroups of are convex cocompact in the sense of Farb and Mosher. More generally, if we have a -hyperbolic surface group extension
any quasiisometrically embedded purely pseudo-Anosov subgroup of is convex cocompact in . We also obtain a generalization of a theorem of Scott and Swarup by showing that finitely generated subgroups of are quasiisometrically embedded in hyperbolic extensions .
Cite this article
Spencer Dowdall, Richard P. Kent IV, Christopher J. Leininger, Pseudo-Anosov subgroups of fibered 3-manifold groups. Groups Geom. Dyn. 8 (2014), no. 4, pp. 1247–1282
DOI 10.4171/GGD/302