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Matings of cubic polynomials with a fixed critical point, Part I: Thurston obstructions


Author: Thomas Sharland
Journal: Conform. Geom. Dyn. 23 (2019), 205-220
MSC (2010): Primary 37F10; Secondary 37F20
DOI: https://doi.org/10.1090/ecgd/342
Published electronically: October 30, 2019
MathSciNet review: 4024933
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Abstract: We prove that if $ F$ is a degree $ 3$ Thurston map with two fixed critical points, then any irreducible obstruction for $ F$ contains a Levy cycle. As a corollary, it will be shown that if $ f$ and $ g$ are two postcritically finite cubic polynomials each having a fixed critical point, then any obstruction to the mating $ f \perp \! \! \! \perp g$ contains a Levy cycle. We end with an appendix to show examples of the obstructions described in the paper.


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Additional Information

Thomas Sharland
Affiliation: Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881
Email: tsharland@uri.edu

DOI: https://doi.org/10.1090/ecgd/342
Received by editor(s): June 26, 2018
Received by editor(s) in revised form: August 27, 2019, and September 18, 2019
Published electronically: October 30, 2019
Article copyright: © Copyright 2019 American Mathematical Society