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On isomorphic classical diffeomorphism groups. I

Author: Augustin Banyaga
Journal: Proc. Amer. Math. Soc. 98 (1986), 113-118
MSC: Primary 58D05; Secondary 22E65, 57R50
MathSciNet review: 848887
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Abstract: Let $ ({M_i},{\alpha _i})$, $ i = 1,2$, be two smooth manifolds equipped with symplectic, contact or volume forms $ {\alpha _i}$. We show that if a group isomorphism between the automorphism groups of $ {\alpha _i}$ is induced by a bijective map between $ {M_i}$, then this map must be a $ {C^\infty }$ diffeomorphism which exchanges the structures $ {\alpha _i}$. This generalizes a theorem of Takens.

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Keywords: Automorphism of a geometric structure, Erlanger Program, symplectic forms, volume forms, contact structures, $ \omega $-transitivity
Article copyright: © Copyright 1986 American Mathematical Society

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