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DESCRIPTION:Title: Perfect kernel of generalized Baumslag-Solitar groups\n
 \nAbstract: Endowed with the Chabauty topology\, the space of subgroups Su
 b(G) of any infinite countable group G is a closed subset of the Cantor sp
 ace\, on which G acts by conjugation. The perfect kernel of G is the large
 st closed subset of Sub(G) without isolated points. It is invariant by con
 jugation.\n	In this talk\, we will see how the action of a group G on an or
 iented tree T can give information on the perfect kernel of G\, and on the
  dynamics induced by the action by conjugation on it. In 2023\, Azuelos an
 d Gaboriau studied the case where the stabilizers 'vanish'\, i.e. there ex
 ists an edge path of T whose stabilizer is finite. They proved that the cl
 osure of the G-invariant subset Sub|•\T|∞(G)\, which consists in the set o
 f subgroups of G acting on T with infinitely many orbits of edges\, is inc
 luded in the perfect kernel and contains a dense orbit.\n	Generalizing resu
 lts obtained by Carderi\, Gaboriau\, Le Maître and Stalder\, we will study
  the space of subgroups of generalized Baumslag-Solitar groups\, i.e. grou
 ps acting cocompactly on an oriented tree with infinite cyclic edge and ve
 rtex stabilizers. These are typical examples of non vanishing stabilizers.
 \n	After proving that the perfect kernel of such non amenable group exactly
  consists in Sub|•\T|∞(G)\, we show that this leads to very different dyna
 mics on it. In particular\, we show the existence of an infinite countable
  G-invariant partition of the perfect kernel such that:\n	- one piece of th
 e decomposition is closed\, and all the other ones are open (and closed if
 f G is virtually the direct product of a free group with ℤ)\;\n	- there exi
 sts a dense orbit in each of these pieces.\n\n \n
DTSTART:20250218T150000Z
DTEND:20250218T160000Z
LOCATION:Room 1120\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Sasha Bontemps (ENS de Lyon)
URL:https://www.mcgill.ca/mathstat/channels/event/sasha-bontemps-ens-de-lyo
 n-363703
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