  The micro-support of sheaves is a tool to describe local propagation results.
A natural problem is then to give sufficient conditions to get global
propagation results from the knowledge of the micro-support. This is the aim of
this paper. As an application, we consider the problem of global existence for
solutions to hyperbolic systems (in the hyperfunction and distribution case),
along the lines of Leray. Causal manifolds, and in particular homogeneous
causal manifolds as considered by Faraut et al., give examples of manifolds to
which our results apply.
