  In four dimensions the topology of the event horizon of an asymptotically
flat stationary black hole is uniquely determined to be the two-sphere $S^2$.
We consider the topology of event horizons in higher dimensions. First, we
reconsider Hawking's theorem and show that the integrated Ricci scalar
curvature with respect to the induced metric on the event horizon is positive
also in higher dimensions. Using this and Thurston's geometric types
classification of three-manifolds, we find that the only possible geometric
types of event horizons in five dimensions are $S^3$ and $S^2 \times S^1$. In
six dimensions we use the requirement that the horizon is cobordant to a
four-sphere (topological censorship), Friedman's classification of topological
four-manifolds and Donaldson's results on smooth four-manifolds, and show that
simply connected event horizons are homeomorphic to $S^4$ or $S^2\times S^2$.
We find allowed non-simply connected event horizons $S^3\times S^1$ and
$S^2\times \Sigma_g$, and event horizons with finite non-abelian first homotopy
group, whose universal cover is $S^4$. Finally, following Smale's results we
discuss the classification in dimensions higher than six.
