Divisibility of the stable Miller-Morita-Mumford classes

Galatius, Soren; Madsen, Ib; Tillmann, Ulrike

doi:10.1090/S0894-0347-06-00523-6

Divisibility of the stable Miller-Morita-Mumford classes
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by Soren Galatius, Ib Madsen and Ulrike Tillmann

J. Amer. Math. Soc. 19 (2006), 759-779

DOI: https://doi.org/10.1090/S0894-0347-06-00523-6

Published electronically: March 17, 2006

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Abstract:

We determine the sublattice generated by the Miller-Morita- Mumford classes $\kappa _i$ in the torsion free quotient of the integral cohomology ring of the stable mapping class group. We further decide when the mod $p$ reductions $\kappa _i \in H^* (B\Gamma _\infty ; \mathbb F_p)$ vanish.

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