Distortion in transformation groups

Calegari, Danny¹ ; Freedman, Michael H²

¹ Department of Mathematics, California Institute of Technology, Pasadena CA 91125, USA
² Microsoft Research, 1 Microsoft Way, Redmond WA 98052, USA

Geometry & topology, Tome 10 (2006) no. 1, pp. 267-293.

Résumé

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.

Détail

DOI : 10.2140/gt.2006.10.267

Keywords: distortion, transformation groups, Pixton action, Bergman property

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