Suppose $Y$ is a topological space were obtained by pasting solid Torus to itself via the boundary map $F:S^1\times S^1\to S^1\times S^1$, $F(z,w)=(z^aw^b,z^cw^d)$ where $a,b,c,d\in\mathbb{Z}$ and $ad-bc=1$.
I) Show that $F$ is a diffeomorphism.
II) what can say about the $Y$(for example about fundamental group of $Y$ respect to $a,b,c,d\in\mathbb{Z}$)?
