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Isomorphisms between diffeomorphism groups

Published online by Cambridge University Press:  19 September 2008

R. P. Filipkiewicz
R. P. Filipkiewicz
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 1AL, England
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Abstract

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It is shown that any group isomorphism between the Ck diffeomorphism groups of two finite-dimensional, boundaryless paracompact manifolds is induced by a Ck diffeomorphism between the manifolds (1 ≤ k ≤ ∞).

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 2 , Issue 2 , June 1982 , pp. 159 - 171
Copyright
Copyright © Cambridge University Press 1982

References

REFERENCES

[1]Whittaker, J. V.. On isomorphic groups and homeomorphic spaces. Ann. Math. 78 (1963), pp. 74–91.CrossRefGoogle Scholar
[2]Takens, F.. Characterization of a differentiable structure by its group of diffeomorphisms. Boletim da Sociedade Brasiliera de Mathematica 10 No. 1 (1979), pp.17–25.CrossRefGoogle Scholar
[3]Montgomery, D. & Zippin, L.. Topobgical Transformation Groups. Wiley: Chichester, 1955.Google Scholar
[4]Rubin, R.. On the reconstruction of topological spaces from their groups of homeomorphisms. Preprint, Ben Gurion University of the Negev, Israel (1980).Google Scholar
[5]Rubin, R.. On the reconstruction of differentiable, Lipschitz, and uniformly continuous manifolds from their groups of homeomorphisms. Abstract communicated to D. B. A. Epstein, Ben Gurion University of the Negev, Israel (1981).Google Scholar
[6]Palis, J. & Smale, S.. Structural stability theorems. Proc. Symp. in Pure Math. 14, Amer. Math. Soc. 1970, pp. 223–231.Google Scholar
[7]Epstein, D. B. A.. The simplicity of certain groups of homeomorphisms. Compositio Mathematica 22 (1970), pp. 165–173.Google Scholar
[8]de Rham, G.. Varietes Differentiables. Herman: Paris, 1960.Google Scholar