Nearly Euclidean Thurston maps
James W. Cannon, William J. Floyd, Walter R. Parry, Kevin M. Pilgrim

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.
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