Topological obstructions to nonnegative curvature
  We find new obstructions to the existence of complete Riemannian metric of nonnegative sectional curvature on manifolds with infinite fundamental groups. In particular, we construct many examples of vector bundles whose total spaces admit no nonnegatively curved metric. 
Igor Belegradek (McMaster University), Vitali Kapovitch (UPenn)