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Journal of the London Mathematical Society Advance Access originally published online on September 16, 2009
Journal of the London Mathematical Society 2009 80(3):665-679; doi:10.1112/jlms/jdp048
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© 2009 London Mathematical Society

Segal's conjecture and the Burnside rings of fusion systems

Antonio Díaz

Department of Mathematical Sciences
University of Copenhagen
Universitetsparken 5
DK-2100 Copenhagen
Denmark
adiaz@math.ku.dk

Assaf Libman

Department of Mathematical Sciences
King's College
University of Aberdeen
Aberdeen AB24 3UE
Scotland
United Kingdom

For a given saturated fusion system F we define the ring A(S)F of the F-invariants of the Burnside ring functor. We show how this ring is related to the Burnside ring of the fusion system F and how it appears naturally in the analogue of Segal's conjecture for the classifying spectrum BF. We give an explicit description of A(S)F and we prove it is a local ring.

2000 Mathematics Subject Classification 55Q55, 19A22, 20C20.

The authors were supported by an EPSRC grant EP/D506484/1.

Received September 5, 2008; revised March 24, 2009; published online September 16, 2009.


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