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Unboundedness of some higher Euler classes (1709.03359v2)
Published 11 Sep 2017 in math.GT
Abstract: 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 $\mathrm{Homeo}_0(S1)\delta$, these Euler classes for $\mathrm{Homeo}_0(M3)\delta$ are unbounded classes. In fact, we give examples of flat topological M bundles over a genus 3 surface whose Euler class takes arbitrary values.