Modular groups, Hurwitz classes and dynamic portraits of NET maps
Document Type
Article
Publication Date
2019
Department/School
Mathematics
Publication Title
Groups, Geometry, and Dynamics
Abstract
An orientation-preserving branched covering f W S2 ! S2 is a nearly Euclidean Thurston (NET) map if each critical point is simple and its postcritical set has exactly four points. Inspired by classical, non-dynamical notions such as Hurwitz equivalence of branched covers of surfaces, we develop invariants for such maps. We then apply these notions to the classification and enumeration of NET maps. As an application, we obtain a complete classification of the dynamic critical orbit portraits of NET maps.
Link to Published Version
Recommended Citation
Floyd, W., Parry, W., & Pilgrim, K. (2018). Modular groups, Hurwitz classes and dynamic portraits of NET maps. Groups, Geometry, and Dynamics, 13(1), 47–88. https://doi.org/10.4171/GGD/479