Distortion in transformation groups

Details Distortion in transformation groups Distortion in transformation groups

2005-09-29

arxiv.org/abs/math/0509701v7

Geom. Topol. 10 (2006) 267-293

Mathematics

Dynamical Systems

This is the version published by Geometry & Topology on 26 March 2006 (V7: typesetting corrections)

Scientific paper

10.2140/gt.2006.10.267

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.

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