Volume 25, issue 1 (2021)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 25
Issue 5, 2167–2711
Issue 4, 1631–2166
Issue 3, 1087–1630
Issue 2, 547–1085
Issue 1, 1–546

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
A vanishing theorem for tautological classes of aspherical manifolds

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

Geometry & Topology 25 (2021) 47–110

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.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

aspherical closed manifolds, tautological classes, characteristic classes, manifold bundles, Burghelea's conjecture
Mathematical Subject Classification 2010
Primary: 55R20, 55R40, 55R60, 57P10
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
Fabian Hebestreit
Mathematical Institute
University of Bonn
Markus Land
Department of Mathematical Sciences
University of Copenhagen
Wolfgang Lück
Mathematical Institute
University of Bonn
Oscar Randal-Williams
Centre for Mathematical Sciences
University of Cambridge
United Kingdom