The homotopy type of the space of diffeomorphisms. I

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A new proof is given of the unpublished results of Morlet on the relation between the homeomorphism group and the diffeomorphism group of a smooth manifold.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.