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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The homotopy type of the space of diffeomorphisms. I
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by Dan Burghelea and Richard Lashof
Trans. Amer. Math. Soc. 196 (1974), 1-36
DOI: https://doi.org/10.1090/S0002-9947-1974-0356103-2

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A new proof is given of the unpublished results of Morlet on the relation between the homeomorphism group and the diffeomorphism group of a smooth manifold.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.
References
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Bibliographic Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 196 (1974), 1-36
  • MSC: Primary 57E05; Secondary 58D05
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0356103-2
  • MathSciNet review: 0356103