Distortion in transformation groups
Dynamical Systems
2009-04-22 v7 Group Theory
Geometric Topology
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.
Cite
@article{arxiv.math/0509701,
title = {Distortion in transformation groups},
author = {Danny Calegari and Michael H Freedman},
journal= {arXiv preprint arXiv:math/0509701},
year = {2009}
}
Comments
This is the version published by Geometry & Topology on 26 March 2006 (V7: typesetting corrections)