Rigidity and characteristic classes of smooth bundles with nonpositively curved fibers

Abstract

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.

26 pages. We fix a mistake in the proof of Thm G. We thank Oscar Randal-Williams for pointing it out. Changes in some proofs, mainly in Sections 2 and 4. Theorems G an H in older versions are now labeled Lemma 4.4 and Theorem G respectively. Theorem F is stated in more generality. Examples, remarks and references added. We thank the referee for their suggestions

References in corpus (1)

• Tautological rings for high dimensional manifolds

Cited by in corpus (4)

• A vanishing theorem for tautological classes of aspherical manifolds
• On the topology of moduli spaces of non-negatively curved Riemannian metrics
• Tautological classes of definite 4-manifolds
• Tautological rings and stabilisation