  In this paper, we study Euler classes in groups of homeomorphisms of Seifert
fibered 3-manifolds. We show that, in contrast to the familiar Euler class for
$\mathrm{Homeo}_0(S^1)^\delta$, these Euler classes for
$\mathrm{Homeo}_0(M^3)^\delta$ are unbounded classes. In fact, we give examples
of flat topological M bundles over a genus 3 surface whose Euler class takes
arbitrary values.
