Rationality is decidable for nearly Euclidean Thurston maps

Authors

William Floyd, Virginia Polytechnic Institute and State University
Walter Parry, Eastern Michigan University
Kevin M. Pilgrim, Indiana University Bloomington

Document Type

Article

Publication Date

2021

Department/School

Mathematics

Publication Title

Geometriae Dedicata

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.

Link to Published Version

10.1007/s10711-020-00593-9

Recommended Citation

Floyd, W., Parry, W., & Pilgrim, K. M. (2021). Rationality is decidable for nearly Euclidean Thurston maps. Geometriae Dedicata, 213(1), 487–512. https://doi.org/10.1007/s10711-020-00593-9