Algebraic & Geometric Topology

Classifying spectra of saturated fusion systems

Kári Ragnarsson

Full-text: Open access

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

Permanent link to this document
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

Subjects
Primary: 55R35: Classifying spaces of groups and $H$-spaces
Secondary: 20D20: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure 55P42: Stable homotopy theory, spectra

Keywords
fusion systems p-local finite groups stable homotopy transfer

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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