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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 which are all invariant and weakly mixing with respect to the action of Aut.
Moreover, for amenable groups , we obtain that the standard co-induction operation from the space of weak equivalence classes of to the space of weak equivalence classes of is continuous if and only if or core is trivial. For general groups we obtain that the co-induction operation is not continuous when . This answers a question raised by Burton and Kechris in . Independently such an answer was also obtained, using a different method, by Bernshteyn in .
Cite this article
Alexander S. Kechris, Vibeke Quorning, Co-induction and invariant random subgroups. Groups Geom. Dyn. 13 (2019), no. 4, pp. 1151–1193