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Topological volumes of fibrations: a note on open covers

Part of: Homology and cohomology theories Global differential geometry

Published online by Cambridge University Press:  11 October 2021

Clara Löh Open the ORCID record for Clara Löh [Opens in a new window]  and
Marco Moraschini Open the ORCID record for Marco Moraschini [Opens in a new window]
Clara Löh
Affiliation:
Fakultät für Mathematik, Universität Regensburg, Regensburg, Germany ([email protected], [email protected])
Marco Moraschini
Affiliation:
Fakultät für Mathematik, Universität Regensburg, Regensburg, Germany ([email protected], [email protected])
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Abstract

We establish a straightforward estimate for the number of open sets with fundamental group constraints needed to cover the total space of fibrations. This leads to vanishing results for simplicial volume and minimal volume entropy, e.g., for certain mapping tori.

Keywords

Amenable categoryfibre bundlessimplicial volumeminimal volume entropy

MSC classification

Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Secondary: 55N10: Singular theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 5 , October 2022 , pp. 1340 - 1360
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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