Title

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

Document Type

Article

Date of Original Version

1-1-2019

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 ∐ g contains a Levy cycle. We end with an appendix to show examples of the obstructions described in the paper.

Publication Title

Conformal Geometry and Dynamics

Volume

23

Issue

12

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