10.4171/GGD/479">
 

Title

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

10.4171/GGD/479

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