A refinement of the simple connectivity at infinity of groups
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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.
8p., revised version, Archiv Math. (to appear)
8p., revised version, Archiv Math. (to appear)