Co-induction and invariant random subgroups
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- OA-Co-induction
Accepted author manuscript, 440 KB, PDF document
In this paper we develop a co-induction operation which transforms an invariant random subgroup of a group into an invariant random subgroup of a larger group. We use this operation to construct new continuum size families of non-atomic, weakly mixing invariant random subgroups of certain classes of wreath products, HNN-extensions and free products with amalgamation. By use of small cancellation theory, we also construct a new continuum size family of non-atomic invariant random subgroups of F2 which are all invariant and weakly mixing with respect to the action of Aut(F2). Moreover, for amenable groups Γ ≤ Δ, we obtain that the standard co-induction operation from the space of weak equivalence classes of Δ to the space of weak equivalence classes of Δ is continuous if and only if [Δ : Γ] < ∞ or coreΔ(Γ) is trivial. For general groups we obtain that the co-induction operation is not continuous when [Δ : Γ] = ∞. This answers a question raised by Burton and Kechris in [17]. Independently such an answer was also obtained, using a different method, by Bernshteyn in [8].
Original language | English |
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Journal | Groups, Geometry, and Dynamics |
Volume | 13 |
Issue number | 4 |
Pages (from-to) | 1151-1193 |
Number of pages | 43 |
ISSN | 1661-7207 |
DOIs | |
Publication status | Published - 2019 |
- Co-induction, Invariant random subgroups, Small cancellation, Weak mixing
Research areas
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