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UID:20251103T025659EST-0524naoUk2@132.216.98.100
DTSTAMP:20251103T075659Z
DESCRIPTION:Title: Stallings-Swan's theorem for Borel graphs\, part 1\n\nAb
 stract: We prove that a Borel graph with uniformly bounded degrees of coho
 mological dimension one is Lipschitz equivalent to a Borel acyclic graph\,
  and in particular\, it is treeable. This is an analog of Stallings-Swan's
  theorem that a group of cohomological dimension one is free. The proof us
 es decomposition of Borel graphs which is given by combining Dunwoody's cr
 iterion for accessibility of groups and Tserunyan's descripitive construct
 ion of structure trees. That is\, we show that if a Borel graph with unifo
 rmly bounded degrees satisfies a cohomological assumtion\, then it is esse
 ntially a free product of two Borel graphs\, one of which is acyclic and t
 he other is uniformly at most one-ended. In the first talk\, we explain th
 e main theorem and how it is deduced from the decomposition theorem. In th
 e second talk\, we discuss the construction of structure trees and the pro
 of of the decomposition theorem.\n\n \n\n \n
DTSTART:20251021T153000Z
DTEND:20251021T173000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Hiroki Ishikura (University of Tokyo)
URL:/mathstat/channels/event/hiroki-ishikura-universit
 y-tokyo-368401
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