A completion theorem for fusion systems

Abstract

We show that the twisted K-theory of the classifying space of a p-local finite group is isomorphic to the completion of the Grothendieck group of twisted representations of the fusion system with respect to the augmentation ideal of the representation ring of the fusion system. We use this result to compute the K-theory of the Ruiz-Viruel exotic 7-local finite groups.

arXiv comment22 pages, no figures. Removed and simplified some computations from Section 6. Corrected Lemmas 2.4 and 2.5 and other minor changes

References in corpus (7)

• Loop groups and twisted K-theory I
• All p-local finite groups of rank two for odd prime p
• Construction of 2-local finite groups of a type studied by Solomon and Benson
• Classifying spectra of saturated fusion systems
• Universal twist in Equivariant K-theory for proper and discrete actions
• The Atiyah--Segal completion theorem in twisted K-theory
• Stable splitting and cohomology of p-local finite groups over the extraspecial p-group of order p^3 and exponent p