The homotopy type of spaces of polynomials with bounded multiplicity (Q345170)

For \(n \geq 3\) the authors improve the homotopy stability dimension for the space of all monic polynomials of degree \(d\) in \(\mathbb C [z]\) without roots of multiplicity \(\geq n\) obtained in [the authors with \textit{M. A. Guest}, Fundam. Math. 161, No. 1--2, 93--117 (1999; Zbl 1016.55004)]. The main result relies on a key unstable result whose proof uses the ``Vassiliev spectral sequence induced from the non-degenerate simplicial resolution of the discriminant \(\Sigma^d_n\).'' The paper is well-structured, reviews basic results on stabilisation and summarises the definitions of the non-degenerate simplicial resolution and the associated truncated simplicial resolutions.