### 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 | |

State | Published - Sep 1986 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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*Proceedings of the American Mathematical Society*, vol. 98, no. 1, pp. 113-118. https://doi.org/10.1090/S0002-9939-1986-0848887-5

**On isomorphic classical diffeomorphism groups. I.** / Banyaga, Augustin.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On isomorphic classical diffeomorphism groups. I

AU - Banyaga, Augustin

PY - 1986/9

Y1 - 1986/9

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84968518095&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968518095&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1986-0848887-5

DO - 10.1090/S0002-9939-1986-0848887-5

M3 - Article

AN - SCOPUS:84968518095

VL - 98

SP - 113

EP - 118

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -