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 $p$ –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.

Keywords

fusion systems, p-local finite groups, stable homotopy, transfer

Mathematical Subject Classification 2000

Primary: 55R35

Secondary: 20D20, 55P42

References

Forward citations

Publication

Received: 25 March 2005

Revised: 19 January 2006

Accepted: 26 January 2006

Published: 26 February 2006

Authors

Kári Ragnarsson
Department of Mathematical Sciences University of Aberdeen Aberdeen AB24 3UE UK

Volume 6, issue 1 (2006)

Kári Ragnarsson

Abstract