A vanishing theorem for tautological classes of aspherical manifolds
Algebraic Topology
2021-03-10 v4 Geometric Topology
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.
Keywords
Cite
@article{arxiv.1705.06232,
title = {A vanishing theorem for tautological classes of aspherical manifolds},
author = {Fabian Hebestreit and Markus Land and Wolfgang Lück and Oscar Randal-Williams},
journal= {arXiv preprint arXiv:1705.06232},
year = {2021}
}
Comments
v4: 38 pages, final version, to appear in G&T