Compactification and trees of spheres covers

Arfeux, Matthieu

doi:10.1090/ecgd/309

Compactification and trees of spheres covers
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Conform. Geom. Dyn. 21 (2017), 225-246 Request permission

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

M. Arfeux, Dynamique holomorphe et arbres de sphères, Thèse de l’université Toulouse.
M. Arfeux, Dynamics on Trees of Spheres, Journal of the London Math. Soc. 95 (2017), no. 1, 177–202, DOI 10.1112/jlms.12016.
Matthieu Arfeux, Approximability of dynamical systems between trees of spheres, Indiana Univ. Math. J. 65 (2016), no. 6, 1945–1977. MR 3595486, DOI 10.1512/iumj.2016.65.5823
Lipman Bers, On spaces of Riemann surfaces with nodes, Bull. Amer. Math. Soc. 80 (1974), 1219–1222. MR 361165, DOI 10.1090/S0002-9904-1974-13686-4
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 262240, DOI 10.1007/BF02684599
Reinhard Diestel, Graph theory, 3rd ed., Graduate Texts in Mathematics, vol. 173, Springer-Verlag, Berlin, 2005. MR 2159259
Risako Funahashi and Masahiko Taniguchi, The cross-ratio compactification of the configuration space of ordered points on $\widehat {\Bbb {C}}$, Acta Math. Sin. (Engl. Ser.) 28 (2012), no. 10, 2129–2138. MR 2966959, DOI 10.1007/s10114-012-1185-x