#### Volume 20, issue 3 (2020)

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Unboundedness of some higher Euler classes

### Kathryn Mann

Algebraic & Geometric Topology 20 (2020) 1221–1234
##### Abstract

We study Euler classes in groups of homeomorphisms of Seifert-fibered $3$–manifolds. In contrast to the familiar Euler class for ${Homeo}_{0}\left({S}^{1}\right)$ as a discrete group, we show that these Euler classes for ${Homeo}_{0}\left({M}^{3}\right)$ 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.

##### Keywords
Euler class, Seifert fibered, $3$–manifold, homeomorphism group
##### Mathematical Subject Classification 2010
Primary: 57R20
Secondary: 57M60, 57S25