Co-induction and invariant random subgroups
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- OA-Co-induction
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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].
Originalsprog | Engelsk |
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Tidsskrift | Groups, Geometry, and Dynamics |
Vol/bind | 13 |
Udgave nummer | 4 |
Sider (fra-til) | 1151-1193 |
Antal sider | 43 |
ISSN | 1661-7207 |
DOI | |
Status | Udgivet - 2019 |
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