  Hawking's topology theorem in general relativity restricts the cross-section
of the event horizon of a black hole in $3+1$ dimension to be either spherical
or toroidal. The toroidal case is ruled out by the topology censorship
theorems. In this article, we discuss the generalization of this result to
black holes in $f(R)$ gravity in $3+1$ and higher dimensions. We obtain a
sufficient differential condition on the function $f'(R)$, which restricts the
topology of the horizon cross-section of a black hole in $f(R)$ gravity in
$3+1$ dimension to be either $S^2$ or $S^1 \times S^1$. We also extend the
result to higher dimensional black holes and show that the same sufficient
condition also restricts the sign of the Yamabe invariant of the horizon
cross-section.
