Topologically singular points in the moduli space of Riemann surfaces

Abstract

In 1962 Rauch found the points in the moduli space of Riemann surfaces not having a neighbourhood homeomorphic to a ball. These points are called here topologically singular. We give a different proof of some of the results of Rauch and also determine the topologically singular points in the branch locus of some equisymmetric families of Riemann surfaces.