Equivalences of Classifying Spaces Completed at the Prime Two

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Reduced, tame and exotic fusion systems (2010, background): “ existence of a centric linking system associated to Flies in lim←−3 O(Fc) (ZF), and the obstruction to its uniqueness lies in lim←− 2 O(Fc) (ZF) [BLO2, Proposition 3.1]. The main results in [O1] and [O2] state that these groups vanish whenever Fis the fusion system of a ﬁnite group G. Deﬁnition 2.9”