## Isomorphisms between groups of diffeomorphisms

HTML articles powered by AMS MathViewer

- by Tomasz Rybicki
- Proc. Amer. Math. Soc.
**123**(1995), 303-310 - DOI: https://doi.org/10.1090/S0002-9939-1995-1233982-7
- PDF | Request permission

## Abstract:

It is known that the group of all diffeomorphisms of a manifold determines uniquely the topological and smooth structure of the manifold itself. We specify a possibly large class of diffeomorphism groups which satisfy this property. In particular, so does the group of contact diffeomorphisms.## References

- Augustin Banyaga,
*Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique*, Comment. Math. Helv.**53**(1978), no. 2, 174–227 (French). MR**490874**, DOI 10.1007/BF02566074 - Augustin Banyaga,
*On isomorphic classical diffeomorphism groups. I*, Proc. Amer. Math. Soc.**98**(1986), no. 1, 113–118. MR**848887**, DOI 10.1090/S0002-9939-1986-0848887-5 - Augustin Banyaga,
*On isomorphic classical diffeomorphism groups. II*, J. Differential Geom.**28**(1988), no. 1, 23–35. MR**950553** - Augustin Banyaga, Rafael de la Llave, and C. Eugene Wayne,
*Cohomology equations and commutators of germs of contact diffeomorphisms*, Trans. Amer. Math. Soc.**312**(1989), no. 2, 755–778. MR**935530**, DOI 10.1090/S0002-9947-1989-0935530-7 - R. P. Filipkiewicz,
*Isomorphisms between diffeomorphism groups*, Ergodic Theory Dynam. Systems**2**(1982), no. 2, 159–171 (1983). MR**693972**, DOI 10.1017/s0143385700001486 - John W. Gray,
*Some global properties of contact structures*, Ann. of Math. (2)**69**(1959), 421–450. MR**112161**, DOI 10.2307/1970192 - Akira Koriyama, Yoshiaki Maeda, and Hideki Omori,
*On Lie algebras of vector fields*, Trans. Amer. Math. Soc.**226**(1977), 89–117. MR**431196**, DOI 10.1090/S0002-9947-1977-0431196-5 - John N. Mather,
*Commutators of diffeomorphisms*, Comment. Math. Helv.**49**(1974), 512–528. MR**356129**, DOI 10.1007/BF02566746 - Hideki Omori,
*Infinite dimensional Lie transformation groups*, Lecture Notes in Mathematics, Vol. 427, Springer-Verlag, Berlin-New York, 1974. MR**0431262**, DOI 10.1007/BFb0063400 - J. Palis and S. Smale,
*Structural stability theorems*, Global Analysis (Proc. Sympos. Pure Math., Vols. XIV, XV, XVI, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 223–231. MR**0267603** - M. E. Shanks and Lyle E. Pursell,
*The Lie algebra of a smooth manifold*, Proc. Amer. Math. Soc.**5**(1954), 468–472. MR**64764**, DOI 10.1090/S0002-9939-1954-0064764-3
T. Rybicki, - Floris Takens,
*Characterization of a differentiable structure by its group of diffeomorphisms*, Bol. Soc. Brasil. Mat.**10**(1979), no. 1, 17–25. MR**552032**, DOI 10.1007/BF02588337 - William Thurston,
*Foliations and groups of diffeomorphisms*, Bull. Amer. Math. Soc.**80**(1974), 304–307. MR**339267**, DOI 10.1090/S0002-9904-1974-13475-0 - James V. Whittaker,
*On isomorphic groups and homeomorphic spaces*, Ann. of Math. (2)**78**(1963), 74–91. MR**150750**, DOI 10.2307/1970503

*On nontransitive groups of diffeomorphisms*, preprint.

## Bibliographic Information

- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**123**(1995), 303-310 - MSC: Primary 58D05; Secondary 17B66, 22E65, 57R50
- DOI: https://doi.org/10.1090/S0002-9939-1995-1233982-7
- MathSciNet review: 1233982