Non-slice linear combinations of algebraic knots (Q437816)

Let \(\mathcal C\) be the group of concordance classes of knots in \(S^3\), and let \(\mathcal G\) be the algebraic concordance group. \textit{J. Levine} [Invent. Math. 8, 98--110 (1969); addendum ibid. 8, 355 (1969; Zbl 0179.52401)] defined a surjection \({\mathcal C} \rightarrow {\mathcal G}\). Let \(\mathcal A\) be the subgroup of \(\mathcal C\) that is generated by algebraic knots. The main result of this paper is that there is an infinitely generated free abelian group contained in the intersection of \(\mathcal A\) with the kernel of \({\mathcal C} \rightarrow {\mathcal G}\).NEWLINENEWLINETo put this result in context, it addresses a question of Rudolf [Notices AMS 23, 410 (1970)], `How independent are the knot--cobordism classes of links of plane curve singularities?', by showing a large family of algebraic knots are independent.