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2006 Classifying spectra of saturated fusion systems
Kári Ragnarsson
Algebr. Geom. Topol. 6(1): 195-252 (2006). DOI: 10.2140/agt.2006.6.195

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 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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Kári Ragnarsson. "Classifying spectra of saturated fusion systems." Algebr. Geom. Topol. 6 (1) 195 - 252, 2006. https://doi.org/10.2140/agt.2006.6.195

Information

Received: 25 March 2005; Revised: 19 January 2006; Accepted: 26 January 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1098.55012
MathSciNet: MR2199459
Digital Object Identifier: 10.2140/agt.2006.6.195

Subjects:
Primary: 55R35
Secondary: 20D20, 55P42

Rights: Copyright © 2006 Mathematical Sciences Publishers

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