  We generalize the domain structure for stationary black hole space-times to
include asymptotically de Sitter and Anti-de Sitter space-times. Given a set of
commuting Killing vector fields of a space-time the domain structure lives on
the submanifold of the orbit space on which at least one of the Killing vector
fields has zero norm. In general the domain structure provides topological and
geometrical invariants of black hole space-times that in specific cases have
proven to be a crucial part of a full characterization leading to uniqueness
theorems. In four and five dimensions the domain structure generalizes the rod
structure. We examine in detail the domain structure for four, five, six and
seven-dimensional black hole space-times including a very general class of
spherically symmetric and static black hole space-times as well as the exact
solutions for Kerr-(Anti)-de Sitter black holes. While for asymptotically
Anti-de Sitter space-times the domain structures resemble that of
asymptotically flat space-times, the domain structures of asymptotically de
Sitter space-times are shown to be compact. Finally, we find under certain
assumptions that the horizon topologies for four- and five-dimensional black
holes are restricted by our domain structure analysis.
