It is known from the work of Banados et al that a spacetime with event
horizons (much like the Schwarzschild black hole) can be obtained fro
m (2 + 1)-dimensional anti-de Sitter space through a suitable identifi
cation of points. We point out that this can be done in 3 + 1 dimensio
ns as well. In this way we obtain black holes with event horizons that
are tori or Riemann surfaces of genus higher than one. They can have
either one or two asymptotic regions (with non-standard topology). Loc
ally, the spacetime,is isometric to anti-de Sitter space.