Classifying spectra of saturated fusion systems

Details Classifying spectra of saturated fusion systems Classifying spectra of saturated fusion systems

2005-02-04

arxiv.org/abs/math/0502092v5

Algebr. Geom. Topol. 6 (2006) 195-252

Mathematics

Algebraic Topology

This is the version published by Algebraic & Geometric Topology on 26 February 2006

Scientific paper

10.2140/agt.2006.6.195

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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