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Formes de Seifert et singularités isolées. (French) Zbl 0557.57014

Noeuds, tresses et singularités, C. R. Sémin., Plans-sur-Bex 1982, Monogr. Enseign. Math. 31, 175-190 (1983).
[For the entire collection see Zbl 0527.00017.]
Let K be the link of the germ (H,0) of a complex analytic hypersurface H in \({\mathbb{C}}^{n+1}\) at the origin. One knows examples of isolated hypersurface singularities where the link is a knotted sphere. In the first part of this paper the author studies the conversion. Suppose the link K of (H,0) is a knotted sphere. Then the hypersurface H is smooth at the origin if and only if the cobordism class of K is of finite order. In the second part the author studies the Murasugi number g of an isolated hypersurface singularity (H,0). By definition one knows that \(g\leq \mu\) where \(\mu\) is the Milnor number. For plane curves ones shows that, if the link K is a knotted homology sphere, then equality holds if and only if the hypersurface singularity is simple.
Reviewer: U.Karras

MSC:

57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)
32S05 Local complex singularities
57R90 Other types of cobordism
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57R65 Surgery and handlebodies
57R19 Algebraic topology on manifolds and differential topology

Citations:

Zbl 0527.00017