Cobordisme fibré et approximation d’une sous-variété singulière par des sous-variétés $C^{\infty }$

Didierjean, André

Annales de l'Institut Fourier, Tome 33 (1983) no. 1, pp. 277-306.

Dans cet article, on montre comment le cobordisme d’applications et le cobordisme fibré fournissent les obstructions à des problèmes de lissage topologique de singularités avec un lieu singulier compact. On calcule dans le cas des petites dimensions les groupes de cobordisme fibré. Les résultats connus sur le cobordisme fibré ou sur son image dans le cobordisme d’application permettent le calcul d’un certain nombre de ces obstructions.

In the paper, one shows that the cobordism of maps and the fiber cobordism give the topological obstructions to smoothing singularities of submanifolds. Groups of fiber cobordism in low dimension are calculated. Results on the fiber cobordism give calculation of obstructions to this smoothing.

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