This talk presents an algebraic invariant that measures the degree to which a (non-standard) static or stationary spacetime can exhibit violations of naive expectations on causal structure; for a static spacetime, this invariant ("fundamental cocycle") is a de Rham cohomology class, but for stationary spacetimes it is something of looser structure.  Using this cocycle provides a simple measure for determining whether two events are timelike related, so it leads to classification of a spacetime along the "causal ladder" (globally hyperbolic, strongly causal, etc.).  It has excellent properties with group actions, leading to conclusions about when spacetimes and their covers or quotients have similar causality properties.  In particular, it can be used to create (by means of quotient) spacetimes of desired causality structure, such as cosmic strings on non-flat backgrounds.