  Quite some time ago, at the singularity conference at Carg\`ese 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 $3$.
