On the regular leaf space of the cauliflower

Abstract

We construct a pinching semiconjugacy from a quadratic polynomial $\fc(z)=z^2+c$ with $c \in (0, 1/4)$ to $\fq(z)=z^2+1/4$ on the sphere. By lifting this semiconjugacy to their natural extensions, we investigate the structure of the regular leaf space of $\fq$ in detail.