Abstract:A Thurston map is called nearly Euclidean if its local degree at each critical point is 2 and it has exactly four postcritical points. Nearly Euclidean Thurston (NET) maps are simple generalizations of rational Lattès maps. We investigate when such a map has the property that the associated pullback map on Teichmüller space is constant. We also show that no Thurston map of degree 2 has constant pullback map.
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- Edgar A. Saenz
- Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061
- MR Author ID: 1229083
- Email: email@example.com
- Received by editor(s): July 4, 2015
- Received by editor(s) in revised form: August 16, 2018
- Published electronically: August 21, 2019
- © Copyright 2019 American Mathematical Society
- Journal: Conform. Geom. Dyn. 23 (2019), 147-163
- MSC (2010): Primary 37F10, 37F20
- DOI: https://doi.org/10.1090/ecgd/339
- MathSciNet review: 3994789