Compactification and trees of spheres covers

Matthieu Arfeux (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We already saw in [A1] that the space of dynamically marked rational maps can be identi ed to a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In the following we describe a topology on this space quotiented by the natural action of its group of isomorphisms. This topology corresponds to the previous convergence notion and makes this space compact.

Mots clés: fractions rationnelles marquées; dynamique holomorphe; compactification; arbres de sphères; topologie

Domaines: Systèmes dynamiques [math.DS]

Matthieu Arfeux. Compactification and trees of spheres covers. Conformal Geometry and Dynamics, 2017, 21, pp.225-246. ⟨10.1090/ecgd/309⟩. ⟨hal-01053433v1⟩