Cover of Shifrin Multivariable Mathematics with Manifolds?

Question

Just curious, anyone knows what this image on the cover of Shifrin's textbook is? It doesn't seem to be a manifold.

Answer 1

It's a real picture of (a slice of a portion of) the Riemann surface $z=w^3$. It's a branched covering of the complex plane, but it is actually a $2$-dimensional manifold.