Irreducibility of periodic curves of cubic polynomials

In the moduli space of one variable complex cubic polynomials with a marked critical point, given any $p \ge 1$, we prove that the loci formed by polynomials with the marked critical point periodic of period $p$ is an irreducible curve.  Our methods rely on techniques used to study one-complex-dimensional parameter spaces.  This is joint work with Matthieu Arfeux.

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