2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64826We 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.8p., revised version, Archiv Math. (to appear)Geometric TopologyGroup Theory20 F 32, 57 M 50text