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arXiv · 1812.01066

Rationality is decidable for nearly Euclidean Thurston maps

William Floyd·Walter Parry·Kevin M. Pilgrim
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Abstract

Nearly Euclidean Thurston (NET) maps are described by simple diagrams which admit a natural notion of size. Given a size bound $C$, there are finitely many diagrams of size at most $C$. Given a NET map $F$ presented by a diagram of size at most $C$, the problem of determining whether $F$ is equivalent to a rational function is, in theory, a finite computation. We give bounds for the size of this computation in terms of $C$ and one other natural geometric quantity. This result partially explains the observed effectiveness of the computer program NETmap in deciding rationality.

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William Floyd, Walter Parry, Kevin M. Pilgrim. 2018-12-03. Rationality is decidable for nearly Euclidean Thurston maps. https://arxiv.org/abs/1812.01066

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