ar X iv : 0 80 1 . 20 06 v 1 [ m at h . G T ] 1 4 Ja n 20 08 GEOMETRY AND RIGIDITY OF MAPPING CLASS GROUPS
نویسنده
چکیده
We study the large scale geometry of mapping class groups MCG(S), using hyperbolicity properties of curve complexes. We show that any self quasi-isometry of MCG(S) (outside a few sporadic cases) is a bounded distance away from a left-multiplication, and as a consequence obtain quasi-isometric rigidity for MCG(S), namely that groups quasi-isometric to MCG(S) are virtually equal to it. (The latter theorem was proved by Hamenstädt using different methods). As part of our approach we obtain several other structural results: a description of the tree-graded structure on the asymptotic cone of MCG(S); a characterization of the image of the curve-complex projection map MCG(S) → Q Y ⊆S C(Y ); and a construction of Σ-hulls in MCG(S), an analogue of convex hulls.
منابع مشابه
ar X iv : 0 80 1 . 20 06 v 2 [ m at h . G T ] 3 M ay 2 00 8 GEOMETRY AND RIGIDITY OF MAPPING CLASS GROUPS
We study the large scale geometry of mapping class groups MCG(S), using hyperbolicity properties of curve complexes. We show that any self quasi-isometry of MCG(S) (outside a few sporadic cases) is a bounded distance away from a left-multiplication, and as a consequence obtain quasi-isometric rigidity for MCG(S), namely that groups quasi-isometric to MCG(S) are virtually equal to it. (The latte...
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