## Algebraic & Geometric Topology

### Classifying spectra of saturated fusion systems

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 6, Number 1 (2006), 195-252.

Dates
Revised: 19 January 2006
Accepted: 26 January 2006
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796511

Digital Object Identifier
doi:10.2140/agt.2006.6.195

Mathematical Reviews number (MathSciNet)
MR2199459

Zentralblatt MATH identifier
1098.55012

#### Citation

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

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