Unboundedness of some higher Euler classes

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 ${\mathrm{H}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{o}}_0(S^1{)}^{\delta }$, these Euler classes for ${\mathrm{H}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{o}}_0(M^3{)}^{\delta }$ are unbounded classes. In fact, we give examples of flat topological M bundles over a genus 3 surface whose Euler class takes arbitrary values.