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.

This is the version published by Algebraic & Geometric Topology on 26 February 2006

References in corpus (2)

• A Segal conjecture for p-completed classifying spaces
• Retractive transfers and p-local finite groups

Cited by in corpus (11)

• Saturated fusion systems as idempotents in the double Burnside ring
• Transfer and characteristic idempotents for saturated fusion systems
• A spectral sequence for fusion systems
• A completion theorem for fusion systems
• Vector bundles over classifying spaces of p-local finite groups and Benson-Carlson duality
• Spaces with Noetherian cohomology
• Simple biset functors and double Burnside rings
• Assigning a classifying space to a fusion system up to F-isomorphism
• Mislin's theorem for fusion systems via Mackey functors
• Evaluation maps and transfers for free loop spaces II
• Homology decompositions and groups inducing fusion systems