Unboundedness of some higher Euler classes

Mann, Kathryn

doi:10.2140/agt.2020.20.1221

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Unboundedness of some higher Euler classes

Kathryn Mann

Algebraic & Geometric Topology 20 (2020) 1221–1234

DOI: 10.2140/agt.2020.20.1221

Abstract

We study Euler classes in groups of homeomorphisms of Seifert-fibered $3$ –manifolds. In contrast to the familiar Euler class for ${Homeo}_{0} (S^{1})$ as a discrete group, we show that these Euler classes for ${Homeo}_{0} (M^{3})$ as a discrete group are unbounded classes. In fact, we give examples of flat topological $M$ –bundles over a genus $3$ surface whose Euler class takes arbitrary values.

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Keywords

Euler class, Seifert fibered, $3$–manifold, homeomorphism group

Mathematical Subject Classification 2010

Primary: 57R20

Secondary: 57M60, 57S25

References

Publication

Received: 25 November 2017

Revised: 27 May 2019

Accepted: 23 September 2019

Published: 27 May 2020

Authors

Kathryn Mann
Department of Mathematics Cornell University Ithaca, NY United States

Volume 20, issue 3 (2020)