Bulletin of the American Mathematical Society

Author(s): Dave Benson
Journal: Bull. Amer. Math. Soc. 33 (1996), 189-198.
MSC (1991): Primary 55P
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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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Retrieve articles in Bulletin of the American Mathematical Society with MSC (1991): 55P

Dave Benson
Affiliation: Department of Mathematics, University of Georgia, Athens GA 30602, USA
Email: djb@byrd.math.uga.edu

DOI: 10.1090/S0273-0979-96-00656-8
PII: S 0273-0979(96)00656-8
Keywords: Stable homotopy, stable splitting, classifying space, double Burnside ring
Additional Notes: Partly supported by a grant from the NSF
Copyright of article: Copyright 1996, American Mathematical Society

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