Non-aspherical ends and nonpositive curvature
  We obtain restrictions on the topology of a closed connected manifold B that bounds a (possibly noncompact) manifold whose interior V admits a complete Riemannian metric of nonpositive sectional curvature. If G denotes the fundamental group of B, then a sample result is that B must be aspherical and incompressible if one of the following is true: (1) V has finite volume and G is virtually nilpotent, (2) G is virtually nilpotent and has no proper torsion-free quotients, (3) G is isomorphic to a uniform, irreducible lattice of real rank > 1. 
Igor Belegradek (Georgia Tech) and T. Tam Nguyen Phan (Ohio State   University)
math.DG math.GT