For postcritically finite cubic polynomials where each finite postcritical point has a preimage outside the critical orbits, the profinite geometric iterated monodromy group is finitely invariably generated and determined up to tree automorphism by the ramification portrait.
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Profinite geometric iterated monodromy groups of postcritically finite polynomials in degree 3
For postcritically finite cubic polynomials where each finite postcritical point has a preimage outside the critical orbits, the profinite geometric iterated monodromy group is finitely invariably generated and determined up to tree automorphism by the ramification portrait.