On isomorphic classical diffeomorphism groups. I

Augustin Banyaga

Research output: Contribution to journal › Article

15 Citations (Scopus)

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

Fingerprint

Diffeomorphism Group
Classical Groups
Isomorphic
Smooth Manifold
Bijective
Diffeomorphism
Automorphism Group
Isomorphism
Contact
Generalise
Theorem
Form

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Banyaga, Augustin. / On isomorphic classical diffeomorphism groups. I. In: Proceedings of the American Mathematical Society. 1986 ; Vol. 98, No. 1. pp. 113-118.
@article{556c1c31edf84e9aa8f2eee20bf2fe6b,
title = "On isomorphic classical diffeomorphism groups. I",
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.",
author = "Augustin Banyaga",
year = "1986",
month = "9",
doi = "10.1090/S0002-9939-1986-0848887-5",
language = "English (US)",
volume = "98",
pages = "113--118",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "1",

}

Banyaga, A 1986, 'On isomorphic classical diffeomorphism groups. I', 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.

In: Proceedings of the American Mathematical Society, Vol. 98, No. 1, 09.1986, p. 113-118.

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 -

Banyaga A. On isomorphic classical diffeomorphism groups. I. Proceedings of the American Mathematical Society. 1986 Sep;98(1):113-118. https://doi.org/10.1090/S0002-9939-1986-0848887-5

Access to Document