Distortion in transformation groups
By Danny Calegari, Michael H. Freedman. 2005
46 citations recorded by the source corpus.
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(Sn), thought of as a discrete group. An appendix by Y de Cornulier shows that Homeo(Sn) has the strong boundedness property, recently introduced by G Bergman. This means that every action of the discrete group Homeo(Sn) on a metric space by isometries has bounded orbits.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3c1bafda3e58f6caf366721a3e6820778c48fbb4
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Groups acting on manifolds: around the Zimmer program (2008, background): “An interesting result of Calegari and Freedman shows that this is not true of Diff(S(2)) and that Diff(S(2)) contains subgroups with elements of arbitrarily large distortion [29].”