SOME APPLICATIONS OF DIFFERENTIAL TOPOLOGY IN GENERAL-RELATIVITY

[摘要] 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 cobordisms are equivalent. Furthermore, because the original work on metric homotopy and causality may not be known to a wide audience, we present an overview of the results here.

[发布日期] 1994-05-01

[关键词] DIFFERENTIAL TOPOLOGY;GENERAL RELATIVITY;SPACE-TIME;SPIN-LORENTZ AND PIN-LORENTZ COBORDISM