The Geometry of the Critically Periodic Curves in the Space of Cubic Polynomials

Abstract

We provide an algorithm for computing the Euler characteristic of the curves in consisting of all polynomials with a periodic critical point of period p in the space of critically marked complex cubic polynomials. The curves were introduced in [Milnor 09, Bonifant et al. 10], and the algorithm applies the main results of [DeMarco and Pilgrim 11b]. The output is shown for periods p⩽26.

2000 AMS Subject Classification:

• MSC 2010
• 37F45
• 37F20

Keywords:

• cubic polynomial
• periodic critical point
• Euler characteristic
• tau function
• pictograph