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

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- by Thomas Sharland
- Conform. Geom. Dyn.
**23**(2019), 205-220 - DOI: https://doi.org/10.1090/ecgd/342
- Published electronically: October 30, 2019
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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.## References

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## Bibliographic Information

**Thomas Sharland**- Affiliation: Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881
- MR Author ID: 1008780
- Email: tsharland@uri.edu
- 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
- © Copyright 2019 American Mathematical Society
- Journal: Conform. Geom. Dyn.
**23**(2019), 205-220 - MSC (2010): Primary 37F10; Secondary 37F20
- DOI: https://doi.org/10.1090/ecgd/342
- MathSciNet review: 4024933