  Recently, there have been several applications of differential and algebraic
topology to problems concerned with the global structure of spacetimes. In this
paper, we derive obstructions to the existence of spin-Lorentz and pin-Lorentz
cobordisms and we show that for compact spacetimes with non-empty boundary
there is no relationship between the homotopy type of the Lorentz metric and
the causal structure. We also point out that spin-Lorentz and tetrad cobordism
are equivalent. Furthermore, because the original work [7] on metric homotopy
and causality may not be known to a wide audience, we present an overview of
the results here.
