A vanishing theorem for tautological classes of aspherical manifolds

Fabian Hebestreit; Markus Land; Wolfgang Lück; Oscar Randal-Williams

doi:10.2140/gt.2021.25.47

A vanishing theorem for tautological classes of aspherical manifolds

Fabian Hebestreit, Markus Land, Wolfgang Lück, Oscar Randal-Williams

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	47-110
Number of pages	64
Journal	Geometry and Topology
Volume	25
Issue number	1
DOIs	https://doi.org/10.2140/gt.2021.25.47
Publication status	Published - 2 Mar 2021
Externally published	Yes

Bibliographical note

Funding Information:
Hebestreit and Land enjoyed support of the CRC 1085 “Higher invariants” at the University of Regensburg. Hebestreit and Lück are members of the Hausdorff Centre for Mathematics, DFG GZ 2047/1, project ID 390685813 at the University of Bonn. Lück and Land were supported by the ERC-grant 662400 “KL2MG-interactions”. Randal-Williams was supported by EPSRC grant EP/M027783/1 “Stable and unstable cohomology of moduli spaces”.

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https://doi.org/10.48550/arXiv.1705.06232

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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.",

author = "Fabian Hebestreit and Markus Land and Wolfgang L{\"u}ck and Oscar Randal-Williams",

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A vanishing theorem for tautological classes of aspherical manifolds

Abstract

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