Rigidity and characteristic classes of smooth bundles with nonpositively   curved fibers
  We prove vanishing results for the generalized Miller-Morita-Mumford classes of some smooth bundles whose fiber is a closed manifold that supports a nonpositively curved Riemannian metric. We also find, under some extra conditions, that the vertical tangent bundle is topologically rigid. 
Mauricio Bustamante, F.Thomas Farrell, Yi Jiang
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