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SUMMARY:On the Measure Equivalence of Baumslag-Solitar Groups and T(r\,s) 
 Tree Automorphism Groups - Damien Gaboriau (CNRS (Centre national de la re
 cherche scientifique))
DTSTART:20250709T104500Z
DTEND:20250709T114500Z
UID:TALK232840@talks.cam.ac.uk
DESCRIPTION:In 2001\, K. Whyte demonstrated that all Baumslag-Solitar grou
 ps BS(r\,s)\, with |r|\,|s|&ne\;1 and |r|&ne\;|s|\, are quasi-isometric\, 
 thus completing the quasi-isometric classification of Baumslag-Solitar gro
 ups initiated by B. Farb and L. Mosher. Since then\, the question of their
  measure equivalence has remained an open and intriguing problem. With A. 
 Poulin\, A. Tserunyan\, R. Tucker-Drob\, and K. Wrobel\, we have solved th
 is problem\, thus establishing the counterpart of Whyte's theorem in terms
  of measured equivalence. To do this we are led to a detour through the wo
 rld of non-unimodular groups and actions which preserve only a class of me
 asure (type III) and we reduce the question to a problem of the theory of 
 measured graphs in this framework.
LOCATION:Seminar Room 1\, Newton Institute
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