Irreducibility of the set of cubic polynomials with one periodic critical point

Abstract

The space of monic centered cubic polynomials with marked critical points is isomorphic to C^2. For each n>0, the locus Sn formed by all polynomials with a specified critical point periodic of exact period n forms an affine algebraic set. We prove that Sn is irreducible, thus giving an affirmative answer to a question posed by Milnor. (This manuscript has been withdrawn)

The authors decided to withdraw this manuscript from arXiv since the proof of the main result relies on "Polynomial Type Theorem" (p6). Recently we have been informed of a gap in the proof of it