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SUMMARY:First order rigidity of manifold diffeomorphism groups - Sang-hyun
  Kim (Korea Institute for Advanced Study (KIAS))
DTSTART:20250710T153000Z
DTEND:20250710T163000Z
UID:TALK232852@talks.cam.ac.uk
DESCRIPTION:Two groups are elementarily equivalent if they have the same s
 ets of true first order group theoretic sentences. We prove that for two r
 eal numbers r\,s &ge\;&nbsp\;1\, and for two smooth closed manifolds M and
  N\, the C^r diffeomorphism group of M is elementarily equivalent to the C
 ^s diffeomorphism group of N if and only if r=s and M is diffeomorphic to 
 N. In the case of r=s=0\, we can even weaken the hypothesis so that the ma
 nifolds are only assumed to be compact\, dropping the smoothability or clo
 sedness hypotheses. This strengthens (1) Whittaker&rsquo\;s theorem (1963)
  on the C^0 case\, and (2) Takens--Filipkiewicz theorems (1982) on C^p cas
 e with an integer p. Joint work with Thomas Koberda (UVa) and Javier de la
  Nuez-Gonzalez (KIAS)
LOCATION:Seminar Room 1\, Newton Institute
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