|
|||||
|
|
|
|
|
|
|
|
|
Geometry and rigidity of
mapping class groups
Jason Behrstock, Bruce Kleiner, Yair Minsky and Lee Mosher |
|
Geometry & Topology 16 (2012) 781–888
|
Abstract |
|
We study the large scale geometry of mapping class groups , using hyperbolicity properties of curve complexes. We show that any self quasi-isometry of (outside a few sporadic cases) is a bounded distance away from a left-multiplication, and as a consequence obtain quasi-isometric rigidity for , namely that groups quasi-isometric to are equivalent to it up to extraction of finite-index subgroups and quotients with finite kernel. (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 ; a characterization of the image of the curve complex projections map from to ; and a construction of –hulls in , an analogue of convex hulls. |
Keywords
mapping class group, quasi-isometric rigidity, qi rigidity,
curve complex, complex of curves, MCG, asymptotic cone
|
Mathematical Subject Classification 2010
Primary: 20F34, 20F36, 20F65, 20F69
Secondary: 57M50, 30F60
|
References |
Publication
Received: 9 April 2010
Revised: 8 February 2012
Accepted: 8 February 2012
Published: 15 May 2012
Proposed: Benson Farb
Seconded: David Gabai, Danny Calegari
|
Authors |
| Jason Behrstock | |
| The Graduate Center and Lehman
College, CUNY New York NY 10016 USA |
|
| http://comet.lehman.cuny.edu/behrstock | |
| Bruce Kleiner | |
| Department of Mathematics Courant Institute of Mathematical Sciences 251 Mercer Street New York NY 10012-1185 USA |
|
| http://math.nyu.edu/~bkleiner/ | |
| Yair Minsky | |
| Department of Mathematics Yale University 10 Hillhouse Ave New Haven CT 06520-8283 USA |
|
| http://www.math.yale.edu/users/yair | |
| Lee Mosher | |
| Department of Mathematics and
Computer Science Rutgers University Newark Newark NJ 07102 USA |
|
|
