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A
vanishing theorem for tautological classes of aspherical
manifolds
Fabian Hebestreit, Markus Land, Wolfgang Lück and Oscar Randal-Williams |
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Geometry & Topology 25 (2021) 47–110
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Abstract |
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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. |
Keywords
aspherical closed manifolds, tautological classes,
characteristic classes, manifold bundles, Burghelea's
conjecture
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Mathematical Subject Classification 2010
Primary: 55R20, 55R40, 55R60, 57P10
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References |
Publication
Received: 30 July 2018
Revised: 26 November 2019
Accepted: 17 January 2020
Published: 2 March 2021
Proposed: Ulrike Tillmann
Seconded: Haynes R Miller, Ralph Cohen
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Authors |
| Fabian Hebestreit | |
| Mathematical Institute University of Bonn Bonn Germany |
|
| Markus Land | |
| Department of Mathematical
Sciences University of Copenhagen Copenhagen Denmark |
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| Wolfgang Lück | |
| Mathematical Institute University of Bonn Bonn Germany |
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| Oscar Randal-Williams | |
| Centre for Mathematical
Sciences University of Cambridge Cambridge United Kingdom |
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