The geometry of the critically-periodic curves in the space of cubic polynomials
We provide an algorithm for computing the Euler characteristic of the curves $S_p$ in the space of cubic polynomials, consisting of all polynomials with a periodic critical point of period $p$. The curves were introduced in [Milnor, Bonifant-Kiwi-Milnor], and the algorithm applies the main results of [DeMarco-Pilgrim]. The output is shown for periods $p \leq 26$.
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