We study Euler classes in groups of homeomorphisms of Seifert-fibered –manifolds. In contrast to the familiar Euler class for as a discrete group, we show that these Euler classes for as a discrete group are unbounded classes. In fact, we give examples of flat topological –bundles over a genus surface whose Euler class takes arbitrary values.
"Unboundedness of some higher Euler classes." Algebr. Geom. Topol. 20 (3) 1221 - 1234, 2020. https://doi.org/10.2140/agt.2020.20.1221