Homology Decompositions and Groups Inducing Fusion Systems

Assaf Libman and Nora Seeliger

Abstract. We relate the construction of groups which realize saturated fusion
systems and signaliser functors with homology decompositions of p-local finite
groups. We prove that the cohomology ring of Robinson's construction is in
some precise sense very close to the cohomology ring of the fusion system it
realizes.