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.

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Bibliographic Details
Published in:Journal of topology 2016-09, Vol.9 (3), p.934-956
Main Authors: Bustamante, Mauricio, Farrell, F. Thomas, Jiang, Yi
Format: Article
Language:English
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Summary: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.
ISSN:1753-8416
1753-8424
DOI:10.1112/jtopol/jtw015