First order rigidity of manifold diffeomorphism groups

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• Sang-hyun Kim (Korea Institute for Advanced Study (KIAS))
• Thursday 10 July 2025, 16:30-17:30
• Seminar Room 1, Newton Institute.

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NPCW06 - Non-positive curvature and applications

Two groups are elementarily equivalent if they have the same sets of true first order group theoretic sentences. We prove that for two real numbers r,s ≥ 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 manifolds are only assumed to be compact, dropping the smoothability or closedness hypotheses. This strengthens (1) Whittaker’s theorem (1963) on the C^{0 case, and (2) Takens—Filipkiewicz theorems (1982) on C}p case with an integer p. Joint work with Thomas Koberda (UVa) and Javier de la Nuez-Gonzalez (KIAS)

This talk is part of the Isaac Newton Institute Seminar Series series.

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