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The Quarterly Journal of Mathematics Advance Access published online on February 21, 2009
The Quarterly Journal of Mathematics, doi:10.1093/qmath/hap009
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© 2009. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

THE REPRESENTATION OF THE MAPPING CLASS GROUP OF A SURFACE ON ITS FUNDAMENTAL GROUP IN STABLE HOMOLOGY

Ulrike Tillmann{dagger}

Mathematical Institute, Oxford University, 24–29 St. Giles Street, Oxford OX1 3LB, UK

{dagger} E-mail: tillmann{at}maths.ox.ac.uk

Received 2 September 2008; revised 23 January 2009
  Abstract

The natural action of the mapping class group of an orientable or non-orientable surface on its fundamental group induces a group homomorphism into the automorphism group of a free group. In the light of a recent theorem, we determine here the map on stable homology.


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