Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 6, Number 1 (2006), 195-252.
Classifying spectra of saturated fusion systems
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 –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 –group.
Algebr. Geom. Topol., Volume 6, Number 1 (2006), 195-252.
Received: 25 March 2005
Revised: 19 January 2006
Accepted: 26 January 2006
First available in Project Euclid: 20 December 2017
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Ragnarsson, Kári. Classifying spectra of saturated fusion systems. Algebr. Geom. Topol. 6 (2006), no. 1, 195--252. doi:10.2140/agt.2006.6.195. https://projecteuclid.org/euclid.agt/1513796511