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

TL;DR

This paper develops criteria for associating a classifying space to a fusion system that preserves cohomological properties up to F-isomorphism, extending previous work to broader group contexts.

Contribution

It introduces new criteria for classifying spaces of fusion systems up to F-isomorphism, expanding the scope to discrete p-toral and profinite groups, with applications to the Kan-Thurston Theorem.

Findings

Criteria for a space to have cohomology strongly F-isomorphic to stable elements

Extension of results to fusion systems over discrete p-toral and profinite groups

Applications to the Kan-Thurston Theorem

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.