Topological aspects of the dynamical moduli space of rational maps

Abstract

We investigate the topology of the space of Möbius conjugacy classes of degree d rational maps on the Riemann sphere. We show that it is rationally acyclic and we compute its fundamental group. As a byproduct, we also obtain the ranks of some higher homotopy groups of the parameter space of degree d rational maps allowing us to extend the previously known range. Moreover, we show that this parameter space is not nilpotent.