Constructive geometrization of Thurston maps and decidability of Thurston equivalence
Dynamical Systems
2013-10-08 v1
Abstract
The key result in the present paper is a direct analogue of the celebrated Thurston's Theorem for marked Thurston maps with parabolic orbifolds. Combining this result with previously developed techniques, we prove that every Thurston map can be constructively geometrized in a canonical fashion. As a consequence, we give a partial resolution of the general problem of decidability of Thurston equivalence of two postcritically finite branched covers of the two-sphere.
Keywords
Cite
@article{arxiv.1310.1492,
title = {Constructive geometrization of Thurston maps and decidability of Thurston equivalence},
author = {Nikita Selinger and Michael Yampolsky},
journal= {arXiv preprint arXiv:1310.1492},
year = {2013}
}