Remote Access Conformal Geometry and Dynamics
Green Open Access

Conformal Geometry and Dynamics

ISSN 1088-4173



Compactification and trees of spheres covers

Author: Matthieu Arfeux
Journal: Conform. Geom. Dyn. 21 (2017), 225-246
MSC (2010): Primary 37F20
Published electronically: May 2, 2017
MathSciNet review: 3645509
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2010): 37F20

Retrieve articles in all journals with MSC (2010): 37F20

Additional Information

Matthieu Arfeux
Affiliation: Pontificia Universidad Católica de Valparaíso, Blanco Viel 596, Cerro Barón, Valparaíso, Chile

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