Modular groups, Hurwitz classes and dynamic portraits of NET maps

  • William Floyd

    Virginia Tech, Blacksburg, USA
  • Walter Parry

    Eastern Michigan University, Ypsilanti, USA
  • Kevin M. Pilgrim

    Indiana University, Bloomington, USA
Modular groups, Hurwitz classes and dynamic portraits of NET maps cover
Download PDF

A subscription is required to access this article.

Abstract

An orientation-preserving branched covering 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.

Cite this article

William Floyd, Walter Parry, Kevin M. Pilgrim, Modular groups, Hurwitz classes and dynamic portraits of NET maps. Groups Geom. Dyn. 13 (2019), no. 1, pp. 47–88

DOI 10.4171/GGD/479