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SUMMARY:Anush Tserunyan: Quasi-treeable equivalence relations are treeable
DTSTART:20250701T080000Z
DTEND:20250701T100000Z
DTSTAMP:20260315T201200Z
UID:indico-event-14426@indico.math.cnrs.fr
DESCRIPTION:Abstract:\nA well-known result from geometric group theory sta
 tes that if a Cayley graph of a finitely generated group is quasi-isometri
 c to a tree\, then the group is virtually free. We prove an analogue of th
 is result in the context of countable Borel equivalence relations\, thereb
 y answering a question posed by R. Tucker-Drob in 2015. Our theorem states
  more generally that if each connected component of a locally finite Borel
  graph 𝐺 is "tree-like" (e.g. is abstractly quasi-isometric to a tree o
 r has bounded treewidth) then there exists an acyclic Borel graph with the
  same connected components as 𝐺. Our proof exploits the Stone duality b
 etween certain families of half-spaces in a graph and median graphs (the 1
 -skeleta of CAT(0) cube complexes)\, via clopen ultrafilters on these fami
 lies of half-spaces. This is joint work with R. Chen\, A. Poulin\, and R. 
 Tao.\n\nhttps://indico.math.cnrs.fr/event/14426/
URL:https://indico.math.cnrs.fr/event/14426/
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