  We give another proof for a result of Brick stating that the simple
connectivity at infinity is a geometric property of finitely presented groups.
This allows us to define the rate of vanishing of $\p1i$ for those groups which
are simply connected at infinity. Further we show that this rate is linear for
cocompact lattices in nilpotent and semi-simple Lie groups, and in particular
for fundamental groups of geometric 3-manifolds.
