True trees are dense
Complex Variables
2020-07-09 v1
Abstract
We show that any compact, connected set in the plane can be approximated by the critical points of a polynomial with two critical values. Equivalently, can be approximated in the Hausdorff metric by a true tree in the sense of Grothendieck's dessins d'enfants.
Cite
@article{arxiv.2007.04062,
title = {True trees are dense},
author = {Christopher J. Bishop},
journal= {arXiv preprint arXiv:2007.04062},
year = {2020}
}
Comments
25 pages, 15 figures