Volume 20, issue 3 (2020)

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Unboundedness of some higher Euler classes

Kathryn Mann

Algebraic & Geometric Topology 20 (2020) 1221–1234

We study Euler classes in groups of homeomorphisms of Seifert-fibered 3–manifolds. In contrast to the familiar Euler class for Homeo0(S1) as a discrete group, we show that these Euler classes for Homeo0(M3) 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.

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Euler class, Seifert fibered, $3$–manifold, homeomorphism group
Mathematical Subject Classification 2010
Primary: 57R20
Secondary: 57M60, 57S25
Received: 25 November 2017
Revised: 27 May 2019
Accepted: 23 September 2019
Published: 27 May 2020
Kathryn Mann
Department of Mathematics
Cornell University
Ithaca, NY
United States