For finite-type spaces with a C2-action, having a conjugation frame is equivalent to being homologically pure, meaning X ∧ HF splits as a wedge of sign-representation suspensions of HF.
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Conjugation Spaces are Cohomologically Pure
For finite-type spaces with a C2-action, having a conjugation frame is equivalent to being homologically pure, meaning X ∧ HF splits as a wedge of sign-representation suspensions of HF.