Many classical spacetimes models are stationary: there's an isometric
**R**-action with timelike orbits. Simplest examples are metric products of
a timelike line with a Riemannian manifold (in fact, those are static:
the orbits have integrable perp-spaces); general structure is that of a
line-bundle over the space of stationary orbits. There can be
"unexpected" deviations from simple causal structure: a photon taking
longer to go one way around a track than the other way. Measuring these
deviations allows for a complete categorization of the global causal
structure, such as being strongly causal. The algebraic tool that does
this is a cohomology class for static spacetimes, but something looser
otherwise, a "cocycle" operating on cycles (loops).