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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The homotopy type of the space of diffeomorphisms. I


Authors: Dan Burghelea and Richard Lashof
Journal: Trans. Amer. Math. Soc. 196 (1974), 1-36
MSC: Primary 57E05; Secondary 58D05
MathSciNet review: 0356103
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Abstract: A new proof is given of the unpublished results of Morlet on the relation between the homeomorphism group and the diffeomorphism group of a smooth manifold.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 $ {\operatorname{Diff}}({D^n},\partial ) \simeq {\Omega ^{n + 1}}({\text{Top}_n}/{O_n})$ is obtained. The main technique is fibrewise smoothing.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0356103-2
PII: S 0002-9947(1974)0356103-2
Article copyright: © Copyright 1974 American Mathematical Society