Michel, F. 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 Cited in 1 ReviewCited in 1 Document 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 Keywords:links of isolated hypersurfaces singularities; simple singularity; link cobordism; Murasugi number; Milnor number; knotted homology sphere Citations:Zbl 0527.00017 PDFBibTeX XML