On isomorphic classical diffeomorphism groups. I

Augustin Banyaga

doi:10.1090/S0002-9939-1986-0848887-5

On isomorphic classical diffeomorphism groups. I

Augustin Banyaga

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Abstract

Let (M_i, α_i), i = 1, 2, be two smooth manifolds equipped with symplectic, contact or volume forms α_i. We show that if a group isomorphism between the automorphism groups of α_i is induced by a bijective map between MM_i, then this map must be a C^∞ diffeomorphism which exchanges the structures α_i. This generalizes a theorem of Takens.

Original language	English (US)
Pages (from-to)	113-118
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	98
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1986-0848887-5
State	Published - Sep 1986

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-1986-0848887-5

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abstract = "Let (Mi, αi), i = 1, 2, be two smooth manifolds equipped with symplectic, contact or volume forms αi. We show that if a group isomorphism between the automorphism groups of αi is induced by a bijective map between MMi, then this map must be a C∞ diffeomorphism which exchanges the structures αi. This generalizes a theorem of Takens.",

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AB - Let (Mi, αi), i = 1, 2, be two smooth manifolds equipped with symplectic, contact or volume forms αi. We show that if a group isomorphism between the automorphism groups of αi is induced by a bijective map between MMi, then this map must be a C∞ diffeomorphism which exchanges the structures αi. This generalizes a theorem of Takens.

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On isomorphic classical diffeomorphism groups. I

Abstract

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