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Distortion in transformation groups
- Source :
- Geometry and Topology, Geometry and Topology, Mathematical Sciences Publishers, 2006, 10, pp.267-293. 〈10.2140/gt.2006.10.267〉, Geometry and Topology, Mathematical Sciences Publishers, 2006, 10, pp.267-293. ⟨10.2140/gt.2006.10.267⟩, Geom. Topol. 10, no. 1 (2006), 267-293, Geometry and Topology, 2006, 10, pp.267-293. ⟨10.2140/gt.2006.10.267⟩
- Publication Year :
- 2005
- Publisher :
- arXiv, 2005.
-
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.<br />Comment: This is the version published by Geometry & Topology on 26 March 2006 (V7: typesetting corrections)
- Subjects :
- Pure mathematics
Property (philosophy)
Mathematics::Dynamical Systems
[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]
Discrete group
transformation groups
Dynamical Systems (math.DS)
Group Theory (math.GR)
01 natural sciences
[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]
57M60
Bergman property
Mathematics - Geometric Topology
Pixton action
0103 physical sciences
FOS: Mathematics
0101 mathematics
Mathematics - Dynamical Systems
ComputingMilieux_MISCELLANEOUS
Mathematics
Group (mathematics)
22F05
37C85
37C85, 22F05, 37C05, 57M60, 57S25
010102 general mathematics
Geometric Topology (math.GT)
37C05
Mathematics::Geometric Topology
Homeomorphism
Action (physics)
Distortion (mathematics)
Metric space
Bounded function
57S25
010307 mathematical physics
Geometry and Topology
distortion
Mathematics - Group Theory
Caltech Library Services
Subjects
Details
- ISSN :
- 14653060 and 13640380
- Database :
- OpenAIRE
- Journal :
- Geometry and Topology, Geometry and Topology, Mathematical Sciences Publishers, 2006, 10, pp.267-293. 〈10.2140/gt.2006.10.267〉, Geometry and Topology, Mathematical Sciences Publishers, 2006, 10, pp.267-293. ⟨10.2140/gt.2006.10.267⟩, Geom. Topol. 10, no. 1 (2006), 267-293, Geometry and Topology, 2006, 10, pp.267-293. ⟨10.2140/gt.2006.10.267⟩
- Accession number :
- edsair.doi.dedup.....ee3fd62926b2dbdb93af7260c77b3ff8
- Full Text :
- https://doi.org/10.48550/arxiv.math/0509701