The University of Ulm, Germany
Families of branched covers of the Riemann sphere with fixed ramification type may be described via Hurwitz spaces. In this talk, we will consider the case where the Hurwitz space is a Riemann surface and may be viewed as a branched cover of the Riemann sphere. We will review how one can calculate the monodromy of this cover (Hurwitz monodromy) in terms of Nielsen tuples by explicit formulas. Moreover, in certain cases, it is possible to calculate the Hurwitz monodromy of quotients of covers via the Nielsen tuples of the original ones.