zbMATH — the first resource for mathematics

Sur les fibres de Nash de surfaces à singularités isolées. (On the Nash fibres of surfaces with isolated singularities). (French) Zbl 0577.57014
A subset K of a projective plane \(P^ 2\) over \({\mathbb{R}}\) is called a compact star with centre in \(v\in P^ 2\) if K is the image of the canonical projection of a compact star in the upper hemisphere and v is the image of the pole. For every compact star with centre in v there exists a \(C^{\infty}\) surface X in \({\mathbb{R}}^ 3\) with an isolated singularity in 0 such that the star is the Nash fibre of X in 0, \(\bar X\) is homeomorphic to a disc and (X,0) is a Whitney stratification of \(\bar X.\) Furthermore let S be a stratified subspace of \({\mathbb{R}}^ N\) such that for every pair (X,Y) of strata the Hausdorff dimension of the conormal space is less than N-1. Then the Morse functions on S are dense.
Reviewer: K.Dechsler

57R45 Singularities of differentiable mappings in differential topology
57R40 Embeddings in differential topology
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
58A35 Stratified sets
57N80 Stratifications in topological manifolds