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

Sharland, Thomas

doi:10.1090/ecgd/342

Matings of cubic polynomials with a fixed critical point, Part I: Thurston obstructions
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Conform. Geom. Dyn. 23 (2019), 205-220 Request permission

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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