  Two wave fronts $W_1$ and $W_2$ that originated at some points of the
manifold $M^n$ are said to be causally related if one of them passed through
the origin of the other before the other appeared. We define the causality
relation invariant $CR (W_1, W_2)$ to be the algebraic number of times the
earlier born front passed through the origin of the other front before the
other front appeared. Clearly, if $CR(W_1, W_2)\neq 0$, then $W_1$ and $W_2$
are causally related. If $CR(W_1, W_2)= 0$, then we generally can not make any
conclusion about fronts being causally related. However we show that for front
propagation given by a complete Riemannian metric of non-positive sectional
curvature, $CR(W_1, W_2)\neq 0$ if and only if the two fronts are causally
related. The models where the law of propagation is given by a metric of
constant sectional curvature are the famous Friedmann Cosmology models.
  The classical linking number $lk$ is a $Z$-valued invariant of two zero
homologous submanifolds. We construct the affine linking number generalization
$AL$ of the $lk$ invariant to the case of linked $(n-1) $-spheres in the total
space of the unit sphere tangent bundle $(STM)^{2n-1}\to M^n$. For all $M$,
except of odd-dimensional rational homology spheres, $AL$ allows one to
calculate the value of $CR(W_1, W_2)$ from the picture of the two wave fronts
at a certain moment. This calculation is done without the knowledge of the
front propagation law and of their points and times of birth. Moreover, in fact
we even do not need to know the topology of $M$ outside of a part $\bar M$ of
$M$ such that $W_1$ and $W_2$ are null-homotopic in $\bar M$.
