Connectivity and simple connectivity of spaces of differentials

曲线上微分的模空间的几何与数学中一些看似遥远的部分有关，特别是与稳定性条件空间和超椭圆曲线上的扭点问题有关。我们的目标是通过对周期施加条件来研究这些模空间的层和某些叶层的叶的连通性问题，以及通过添加Teichmüler标记来给出覆盖空间的简单连通性的问题。

The geometry of moduli spaces of differentials on curves is connected to a number of seemingly distant parts of mathematics, notably to spaces of stability conditions and to torsion point questions on hyperelliptic curves. Our goal is to investigate connectivity questions for strata of these moduli spaces and leaves of certain foliation given by imposing conditions on periods as well as questions about simple connectivity of the covering spaces given by adding Teichmüller markings.