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The mapping class group of an orientable closed surface with one marked point can be identified, by the Nielsen action, with a subgroup of the group of orientation-preserving homeomorphisms of the circle. This inclusion pulls back the “discrete universal Euler class” producing a non-zero class in the second integral cohomology of the mapping class group. In this largely expository note, we determine the non-vanishing behavior of the powers of this class. Our argument relies on restricting the cohomology classes to torsion subgroups of the mapping class group.
Arnold Mathematical Journal – Springer Journals
Published: Sep 7, 2020
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