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The parameter space $\mathcal{S}_p$ for monic centered cubic polynomial mapswith a marked critical point of period $p$ is a smooth affine algebraic curvewhose genus increases rapidly with $p$. Each $\mathcal{S}_p$ consists of acompact connectedness locus together with finitely many escape regions, each ofwhich is biholomorphic to a punctured disk and is characterized by anessentially unique Puiseux series. This note will describe the topology of$\mathcal{S}_p$, and of its smooth compactification, in terms of these escaperegions. It concludes with a discussion of the real sub-locus of$\mathcal{S}_p$.

Cubic Polynomial Maps with Periodic Critical Orbit, Part II: Escape Regions