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$C^0$-rigidity of Poisson diffeomorphisms (2302.05559v2)

Published 11 Feb 2023 in math.SG

Abstract: We prove the Poisson version of the Gromov-Eliashberg's $C^0$-rigidity. More precisely, we prove that the group of Poisson diffeomorphisms is closed with respect to the $C^0$ topology inside the group of all diffeomorphisms. The proof relies on the Poisson version of the energy-capacity inequality.