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SUMMARY:Subgroup mixing in Baumslag-Solitar groups - Sasha Bontemps (ENS L
 yon)
DTSTART:20260123T134500Z
DTEND:20260123T144500Z
UID:TALK242011@talks.cam.ac.uk
CONTACT:Monika Kudlinska
DESCRIPTION:Endowed with the Chabauty topology\, the space of subgroups of
  any infinite countable group G is a closed subspace of the Cantor set\, e
 quipped with an action by homeomorphisms given by the G-conjugation. We ar
 e interested in the dynamics induced by this action on closed G-invariant 
 subspaces. The largest closed subspace without isolated point is an exampl
 e of such subspace called the perfect kernel of G. In an acylindrically hy
 perbolic context\, Hull\, Mynasyan and Osin demonstrated strong mixing pro
 perties (namely µ-mixing for a suitable measure µ on G\, a strengthening
  of high topological transitivity). We uncover a radically different situa
 tion in the case of non metabelian Baumslag-Solitar groups. For the decomp
 osition of the perfect kernel introduced by Carderi\, Gaboriau\, Le Maîtr
 e and Stalder\, who proved high topological transitivity on each piece\, w
 e show that the conjugation is even µ-mixing in the case of unimodular Ba
 umslag-Solitar groups. On the contrary\, when the group is non unimodular\
 , there exists a continuum of measures µ for which the action is µ-mixin
 g only on a single piece of the partition.
LOCATION:MR13
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