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Stably splitting BG

Author: Dave Benson
Journal: Bull. Amer. Math. Soc. 33 (1996), 189-198
MSC (1991): Primary 55P
MathSciNet review: 1362628
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Abstract: In the early nineteen eighties, Gunnar Carlsson proved the Segal conjecture on the stable cohomotopy of the classifying space $BG$ of a finite group $G$. This led to an algebraic description of the ring of stable self-maps of $BG$ as a suitable completion of the ``double Burnside ring''. The problem of understanding the primitive idempotent decompositions of the identity in this ring is equivalent to understanding the stable splittings of $BG$ into indecomposable spectra. This paper is a survey of the developments of the last ten to fifteen years in this subject.

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Additional Information

Dave Benson
Affiliation: Department of Mathematics, University of Georgia, Athens GA 30602, USA

Keywords: Stable homotopy, stable splitting, classifying space, double Burnside ring
Additional Notes: Partly supported by a grant from the NSF
Article copyright: © Copyright 1996 American Mathematical Society