A vanishing theorem for tautological classes of aspherical manifolds
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Peer-reviewed
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Abstract
Tautological classes, or generalised Miller-Morita-Mumford classes, are basic characteristic classes of smooth fibre bundles, and have recently been used to describe the rational cohomology of classifying spaces of diffeomorphism groups for several types of manifolds. We show that rationally tautological classes depend only on the underlying topological block bundle, and use this to prove the vanishing of tautological classes for many bundles with fibre an aspherical manifold.
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Keywords
math.AT, math.AT, math.GT
Journal Title
Geometry and Topology
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Journal ISSN
1465-3060
1364-0380
1364-0380
Volume Title
25
Publisher
Mathematical Sciences Publishers
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Sponsorship
Engineering and Physical Sciences Research Council (EP/M027783/1)