The homotopy type of the space of diffeomorphisms. I-Reference-Cited by-同舟云学术

The homotopy type of the space of diffeomorphisms. I

Published:1974 Issue:0 Volume:196 Page:1-36
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Burghelea Dan,Lashof Richard

Abstract

A new proof is given of the unpublished results of Morlet on the relation between the homeomorphism group and the diffeomorphism group of a smooth manifold. In particular, the result Diff ( D n , ∂ ) ≃ Ω n + 1 ( Top n / O n ) {\operatorname {Diff}}({D^n},\partial ) \simeq {\Omega ^{n + 1}}({\text {Top}_n}/{O_n}) is obtained. The main technique is fibrewise smoothing.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1974-196-00/S0002-9947-1974-0356103-2/S0002-9947-1974-0356103-2.pdf

Reference26 articles.

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2. The non-finite homotopy type of some diffeomorphism groups;Antonelli, P. L.;Topology,1972

3. \bysame, The concordance-homotopy groups of geometric automorphism groups, Lecture Notes in Math., vol. 215, Springer-Verlag, Berlin and New York.

4. Hilbert manifolds;Burghelea, Dan;Ann. of Math. (2),1969

5. La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie;Cerf, Jean;Inst. Hautes \'{E}tudes Sci. Publ. Math.,1970

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