Cover of a finitely punctured plane Let $X_n$ be the plane with a finite number $n$ of punctures, and let $p : Y \rightarrow X_n$ be a covering map (it may have infinite degree). 
Can we say anything about the topology of $Y$? (I know that $Y$ has a natural structure of Riemann surface).
I should really read properly about the general theory of covering maps, which I only vaguely know. I've heard about a 1 to 1 correspondance between covering maps and automorphisms of the fundamental group (which is here the free group with $n$ generators) but I don't know anymore than that.

$Y$ can be homeomorphic to a punctured Riemann surface ( @studiosus: thanks!). I guess we should think about the Riemann surfaces as they were first conceived.
As to the coverings and fundamental groups, there is a $1-1$ correspondence between ( conjugacy classes of ) subgroups of the fundamental group of $X_n$ and coverings of $X_n$. The fundamental group of $X_n$ is free on $n$ generators. Any subgroup of $\pi_1(X_n)$ is again free. So  you know right away that $\pi_1(Y)$ is again free. 
