On a discriminant knot group problem of Brieskorn

Abstract

Quite some time ago, at the singularity conference at Cargese 1972 Brieskorn asked the following question: Is the local fundamental group $\pi_1^{s}(S-D)$ of the discriminant complement inside the semi-universal unfolding $S$ of an isolated hypersurface singularity constant for $s$ in the $\mu$-constant stratum $\Sigma_E$? We review this question and give an affirmative answer in case of singular plane curve germs of multiplicity at most $3$.