Some applications of differential topology in general relativity

Abstract

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.