Rationality is decidable for nearly Euclidean Thurston maps
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
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