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Divisibility of the stable Miller-Morita-Mumford classes


Authors: Soren Galatius, Ib Madsen and Ulrike Tillmann
Journal: J. Amer. Math. Soc. 19 (2006), 759-779
MSC (2000): Primary 57R20, 55P47
DOI: https://doi.org/10.1090/S0894-0347-06-00523-6
Published electronically: March 17, 2006
MathSciNet review: 2219303
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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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Additional Information

Soren Galatius
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
Email: galatius@math.stanford.edu

Ib Madsen
Affiliation: Matematisk Institut, Aarhus Universitet, 8000 Aarhus C, Denmark
Email: imadsen@imf.au.dk

Ulrike Tillmann
Affiliation: Mathematical Institute, 24-29 St. Giles Street, Oxford OX1 3LB, United Kingdom
Email: tillmann@maths.ox.ac.uk

DOI: https://doi.org/10.1090/S0894-0347-06-00523-6
Keywords: Mapping class group, characteristic classes, surface bundles
Received by editor(s): October 31, 2004
Published electronically: March 17, 2006
Additional Notes: The third author was supported by an Advanced Fellowship of the EPSRC
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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