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Conformal Geometry and Dynamics

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Compactification and trees of spheres covers


Author: Matthieu Arfeux
Journal: Conform. Geom. Dyn. 21 (2017), 225-246
MSC (2010): Primary 37F20
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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Additional Information

Matthieu Arfeux
Affiliation: Pontificia Universidad Católica de Valparaíso, Blanco Viel 596, Cerro Barón, Valparaíso, Chile
Email: matthieu.arfeux@pucv.cl

DOI: https://doi.org/10.1090/ecgd/309
Keywords: Limits of dynamical systems, compactification, rescaling limits, Deligne-Mumford compactification, algebraic geometry, trees of spheres, noded spheres
Received by editor(s): October 14, 2016
Received by editor(s) in revised form: February 10, 2017
Published electronically: May 2, 2017
Article copyright: © Copyright 2017 American Mathematical Society