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
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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 projections mapMCG(S) →
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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
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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تاریخ انتشار 2008