Modular groups, Hurwitz classes and dynamic portraits of NET maps
Modular groups, Hurwitz classes and dynamic portraits of NET maps
An orientation-preserving branched covering f: S^2 \to S^2 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 …