Distortion in transformation groups

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.

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

References in corpus (3)

• Growth of maps, distortion in groups and symplectic geometry
• Strongly bounded groups and infinite powers of finite groups
• A topological version of the Bergman property

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