Volume 10, issue 1 (2006)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Distortion in transformation groups

Danny Calegari and Michael H Freedman

Appendix: Yves de Cornulier

Geometry & Topology 10 (2006) 267–293

arXiv: math.DS/0509701

Abstract

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(Sn), thought of as a discrete group.

An appendix by Y de Cornulier shows that Homeo(Sn) has the strong boundedness property, recently introduced by G Bergman. This means that every action of the discrete group Homeo(Sn) on a metric space by isometries has bounded orbits.

Keywords
distortion, transformation groups, Pixton action, Bergman property
Mathematical Subject Classification 2000
Primary: 37C85
Secondary: 37C05, 22F05, 57S25, 57M60
References
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Publication
Received: 7 October 2005
Accepted: 8 February 2006
Published: 26 March 2006
Proposed: Benson Farb
Seconded: Leonid Polterovich, Robion Kirby
Authors
Danny Calegari
Department of Mathematics
California Institute of Technology
Pasadena CA 91125
USA
Michael H Freedman
Microsoft Research
1 Microsoft Way
Redmond WA 98052
USA
Yves de Cornulier
Institut de Mathématiques
Université de Neuchâtel
Rue Émile Argand 11
CH-2007 Neuchâtel
Switzerland