True trees are dense

Christopher J. Bishop

doi:10.1007/s00222-013-0488-6

True trees are dense

Christopher J. Bishop

Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	433-452
Number of pages	20
Journal	Inventiones Mathematicae
Volume	197
Issue number	2
DOIs	https://doi.org/10.1007/s00222-013-0488-6
State	Published - Aug 2014

Keywords

30C62

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10.1007/s00222-013-0488-6

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

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

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EP - 452

JO - Inventiones Mathematicae

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ER -

True trees are dense

Abstract

Keywords

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