Skip the sphere

Compute the homotopy groups of the compact surfaces.

Drawable 3-manifolds

For an embedded compact 3-manifold $M \subseteq \mathbb{R}^3$, $H_1(M)=0$ implies $\pi_1(M)=0$.

Three-sheeted connected covering spaces of the wedge of three real projective spaces

The title is pretty self-explanatory: the exercise is to classify such coverings.