Compactification and trees of spheres covers

Arfeux, Matthieu

doi:10.1090/ecgd/309

Compactification and trees of spheres covers
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by Matthieu Arfeux

Conform. Geom. Dyn. 21 (2017), 225-246

DOI: https://doi.org/10.1090/ecgd/309

Published electronically: May 2, 2017

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Abstract:

The space of dynamically marked rational maps can be identified with 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 this paper we describe a topology on the quotient of this space under the natural action of its group of isomorphisms. This topology is proved to be consistent with this notion of convergence.

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