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A splitting for the stable mapping class group

Published online by Cambridge University Press:  01 July 1999

ULRIKE TILLMANN
ULRIKE TILLMANN
Affiliation:
Mathematical Institute, Oxford OX1 3LB; e-mail: tillmann@maths.ox.ac.uk
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Abstract

The main result of [15] is that the classifying space of the stable mapping class group after plus construction BΓ+∞ is an infinite loop space. This result is used to show that, localized away from two, a connected component of the stable homotopy groups of spheres QS0 splits off BΓ+∞. The splitting is a splitting of infinite loop spaces. It follows immediately that the homology with coefficients in ℤ[½] of the infinite symmetric group is a direct summand of the homology of the stable mapping class group.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 127 , Issue 1 , July 1999 , pp. 55 - 65
Copyright
The Cambridge Philosophical Society 1999

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