Assigning a classifying space to a fusion system up to F-isomorphism

Abstract

Complementing and extending the Inventiones work of Benson, Grodal, Henke [Group cohomology and control of p−fusion, Invent. Math. 197 (2014), 491-507] we give criteria for a space to have cohomology (strongly) F −isomorphic in the sense of Quillen to the stable elements. We extend results about groups models to fusion systems over discrete p-toral groups and profinite groups and provide various applications to the Kan-Thurston Theorem.