Paper:       Classifying spectra for saturated fusion systems

Author:      Kári Ragnarsson

Institution: Department of Mathematical Sciences,
             University of Aberdeen
             Aberdeen AB243UE
             United Kingdom

Status:      Published in Algebr. Geom. Topol.  6  (2006) 195--252

Abstract: The assignment of classifying spectra to saturated fusion systems
was suggested by Linckelmann and Webb and has been carried out by
Broto, Levi and Oliver. A more rigid (but equivalent) construction
of the classifying spectra is given in this paper. It is shown that
the assignment is functorial for fusion-preserving homomorphi~sms in
a way which extends the assignment of stable $p$-completed
classifying spaces to finite groups, and admits a transfer theory
analogous to that for finite groups. Furthermore the group of
homotopy classes of maps between classifying spectra is described,
and in particular it is shown that a fusion system can be
reconstructed from its classifying spectrum regarded as an object
under the stable classifying space of the underlying $p$-group.