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Distortion in
transformation groups
Danny Calegari and Michael H FreedmanAppendix: Yves de Cornulier |
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Geometry & Topology 10 (2006) 267–293
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arXiv: math.DS/0509701 |
Abstract |
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We exhibit rigid rotations of spheres as distortion elements in groups of diffeomorphisms, thereby answering a question of J Franks and M Handel. We also show that every homeomorphism of a sphere is, in a suitable sense, as distorted as possible in the group Homeo(S, thought of as a discrete group. An appendix by Y de Cornulier shows that Homeo(S has the strong boundedness property, recently introduced by G Bergman. This means that every action of the discrete group Homeo(S on a metric space by isometries has bounded orbits. |
Keywords
distortion, transformation groups, Pixton action, Bergman
property
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Mathematical Subject Classification 2000
Primary: 37C85
Secondary: 37C05, 22F05, 57S25, 57M60
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References |
Forward citations |
Publication
Received: 7 October 2005
Revised: 20 February 2006
Accepted: 8 February 2006
Published: 26 March 2006
Proposed: Benson Farb
Seconded: Leonid Polterovich, Robion Kirby
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Authors |
| Danny Calegari | |
| Department of Mathematics California Institute of Technology Pasadena CA 91125 USA |
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| Michael H Freedman | |
| Microsoft Research 1 Microsoft Way Redmond WA 98052 USA |
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| Yves de Cornulier | |
| Institut de Mathématiques Université de Neuchâtel Rue Émile Argand 11 CH-2007 Neuchâtel Switzerland |
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