no. 2
On the homotopy type of Diff (M n ) and connected problems
Annales de l'Institut Fourier, Tome 23 (1973) no. 2, pp. 3-17.

Cet article est un rapport contenant des résultats sur le type d’homotopie du groupe des difféormorphismes Diff (M n ) d’une variété différentiable compacte M n (munie de la topologie C ∞ ) et sur la comparaison homotopique de cet espace avec le groupe des homéomorphismes de la variété M n (munie de la topologie C o ). Comme applications, on obtient des renseignements nouveaux sur les groupes d’homotopie de Diff (D n ,∂D n ), Top n et Top n /O n et sur le nombre des composantes connexes de l’espace des pseudo-isotopies topologiques et combinatoires.

Les résultats sont énoncés dans les sections 1 et 2 et les idées géométriques sont expliquées dans la section 3.

This paper reports on some results concerning:

a) The homotopy type of the group of diffeomorphisms Diff (M n ) of a differentiable compact manifold M n (with C ∞ -topology).

b) the result of the homotopy comparison of this space with the group of all homeomorphisms Homeo M n (with C o -topology). As a biproduct, one gets new facts about the homotopy groups of Diff (D n ,∂D n ), Top n , Top n /O n and about the number of connected components of the space of topological and combinatorial pseudoisotopies.

The results are contained in Section 1 and Section 2 and the geometric ideas in Section 3.

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Burghelea, Dan. On the homotopy type of ${\rm Diff}(M^n)$ and connected problems. Annales de l'Institut Fourier, Tome 23 (1973) no. 2, pp. 3-17. doi : 10.5802/aif.453. https://aif.centre-mersenne.org/articles/10.5802/aif.453/

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