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Classifying spectra of saturated fusion systems
Kári Ragnarsson
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Algebraic & Geometric Topology 6
(2006) 195–252
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Abstract
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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 homomorphisms 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.
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Keywords
fusion systems, p-local finite groups,
stable homotopy, transfer
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Mathematical Subject Classification
Primary: 55R35
Secondary: 20D20, 55P42
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Publication
Received: 25 March 2005
Revised: 19 January 2006
Accepted: 26 January 2006
Published: 26 February 2006
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