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On dense totipotent free subgroups in full groups
- Source :
- Geometry and Topology, Geometry and Topology, Mathematical Sciences Publishers, In press, Geometry and Topology, In press
- Publication Year :
- 2021
- Publisher :
- HAL CCSD, 2021.
-
Abstract
- We study probability measure preserving (p.m.p.) non-free actions of free groups and the associated IRS's. The perfect kernel of a countable group Gamma is the largest closed subspace of the space of subgroups of Gamma without isolated points. We introduce the class of totipotent ergodic p.m.p. actions of Gamma: those for which almost every point-stabilizer has dense conjugacy class in the perfect kernel. Equivalently, the support of the associated IRS is as large as possible, namely it is equal to the whole perfect kernel. We prove that every ergodic p.m.p. equivalence relation R of cost $<br />Comment: 22 pages. A figure added as well as a few extra details in the proof of the main theorem. Some small typos corrected. To appear in Geometry & Topology
- Subjects :
- IRS
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
non-free actions
Group Theory (math.GR)
Dynamical Systems (math.DS)
Measurable group actions
transitive actions of countable groups
[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]
37A20, 37B05, 22F50, 22F10
ergodic equivalence relations
MSC: 37A20, 22F50, 22F10, 37B05
orbit equivalence
FOS: Mathematics
free groups
Mathematics - Dynamical Systems
Mathematics - Group Theory
space of subgroups
Subjects
Details
- Language :
- English
- ISSN :
- 14653060 and 13640380
- Database :
- OpenAIRE
- Journal :
- Geometry and Topology, Geometry and Topology, Mathematical Sciences Publishers, In press, Geometry and Topology, In press
- Accession number :
- edsair.doi.dedup.....a75d24a6bdcb62ad30b0359beed14bef