Topological aspects of the dynamical moduli space of rational maps

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.

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