  We use a counting argument and surgery theory to show that if $D$ is a
sufficiently general algebraic hypersurface in $\Bbb C^n$, then any local
diffeomorphism $F:X \to \Bbb C^n$ of simply connected manifolds which is a
$d$-sheeted cover away from $D$ has degree $d=1$ or $d=\infty$ (however all
degrees $d > 1$ are possible if $F$ fails to be a local diffeomorphism at even
a single point). In particular, any \'etale morphism $F:X \to \Bbb C^n$ of
algebraic varieties which covers away from such a hypersurface $D$ must be
birational.
