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
DOI: https://doi.org/10.1090/ecgd/309
Published electronically: May 2, 2017
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?)

  • [A] M. Arfeux, Dynamique holomorphe et arbres de sphères, Thèse de l'université Toulouse.
  • [A1] M. Arfeux, Dynamics on Trees of Spheres, Journal of the London Math. Soc. 95 (2017), no. 1, 177-202, DOI 10.1112/jlms.12016.
  • [A2] Matthieu Arfeux, Approximability of dynamical systems between trees of spheres, Indiana Univ. Math. J. 65 (2016), no. 6, 1945-1977. MR 3595486, https://doi.org/10.1512/iumj.2016.65.5823
  • [B] Lipman Bers, On spaces of Riemann surfaces with nodes, Bull. Amer. Math. Soc. 80 (1974), 1219-1222. MR 0361165, https://doi.org/10.1090/S0002-9904-1974-13686-4
  • [DeM] P. Deligne and D. Mumford, The irreducibility of the space of curves of given genus, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 75-109. MR 0262240
  • [Di] Reinhard Diestel, Graph theory, 3rd ed., Graduate Texts in Mathematics, vol. 173, Springer-Verlag, Berlin, 2005. MR 2159259
  • [FT] Risako Funahashi and Masahiko Taniguchi, The cross-ratio compactification of the configuration space of ordered points on $ \widehat {\mathbb{C}}$, Acta Math. Sin. (Engl. Ser.) 28 (2012), no. 10, 2129-2138. MR 2966959, https://doi.org/10.1007/s10114-012-1185-x

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
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

American Mathematical Society