Matings of cubic polynomials with a fixed critical point, part I: Thurston obstructions
Date of Original Version
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.
Conformal Geometry and Dynamics
Sharland, Thomas. "Matings of cubic polynomials with a fixed critical point, part I: Thurston obstructions." Conformal Geometry and Dynamics 23, 12 (2019): 205-220. doi:10.1090/ecgd/342.