Abstract
In this work, we are concerned with the realization of spaces up to rational homotopy as classifying spaces. In this paper, we first show that a class of rank-two rational spaces cannot be realized up to rational homotopy as the classifying space of any n-connected and π-finite space for n≥1. We also show that the Eilenberg-Mac Lane space K(Qr,n)(r≥2,n≥2) can be realized up to rational homotopy as the classifying space of a simply connected and elliptic space X if and only if X has the rational homotopy type of ∏rSn−1 with n even.
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