English

True trees are dense

Complex Variables 2020-07-09 v1

Abstract

We show that any compact, connected set KK in the plane can be approximated by the critical points of a polynomial with two critical values. Equivalently, KK can be approximated in the Hausdorff metric by a true tree in the sense of Grothendieck's dessins d'enfants.

Keywords

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

R2 v1 2026-06-23T16:56:55.454Z