Nearly Euclidean Thurston maps

TL;DR

This paper introduces nearly Euclidean Thurston maps, a new class of maps from the 2-sphere to itself that generalize Euclidean Thurston maps, expanding the understanding of Thurston map classifications.

Contribution

The paper defines and explores nearly Euclidean Thurston maps, providing a broader framework for studying Thurston maps beyond the Euclidean case.

Findings

Characterization of nearly Euclidean Thurston maps

Extension of Euclidean Thurston map properties

Potential applications to Thurston map classification

Abstract

We introduce and study a class of Thurston maps from the 2-sphere to itself which we call nearly Euclidean Thurston (NET) maps. These are simple generalizations of Euclidean Thurston maps.