#### Volume 10, issue 1 (2006)

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Distortion in transformation groups

### 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(S${}^{n}$, thought of as a discrete group.

An appendix by Y de Cornulier shows that Homeo(S${}^{n}$ has the strong boundedness property, recently introduced by G Bergman. This means that every action of the discrete group Homeo(S${}^{n}$ 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