On isomorphic classical diffeomorphism groups. I

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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.

Original languageEnglish (US)
Pages (from-to)113-118
Number of pages6
JournalProceedings of the American Mathematical Society
Volume98
Issue number1
DOIs
StatePublished - Sep 1986

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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