Title: $μ$-constant monodromy groups and Torelli results for the quadrangle singularities and the bimodal series,
Abstract: This paper is a sequel to [He11] and [GH17]. In [He11] a notion of marking of
isolated hypersurface singularities was defined, and a moduli space
$M_\mu^{mar}$ for marked singularities in one $\mu$-homotopy class of isolated
hypersurface singularities was established. It is an analogue of a
Teichmüller space. It comes together with a $\mu$-constant monodromy group
$G^{mar}\subset G_{\mathbb{Z}}$. Here $G_{\mathbb{Z}}$ is the group of
automorphisms of a Milnor lattice which respect the Seifert form. It was
conjectured that $M_\mu^{mar}$ is connected. This is equivalent to $G^{mar}=
G_{\mathbb{Z}}$. Also Torelli type conjectures were formulated. In [He11] and
[GH17] $M_\mu^{mar}, G_{\mathbb{Z}}$ and $G^{mar}$ were determined and all
conjectures were proved for the simple, the unimodal and the exceptional
bimodal singularities. In this paper the quadrangle singularities and the
bimodal series are treated. The Torelli type conjectures are true. But the
conjecture $G^{mar}= G_{\mathbb{Z}}$ and $M_\mu^{mar}$ connected does not hold
for certain subseries of the bimodal series.