Proceedings of the American Mathematical Society
Which spaces occur as a classifying space for fibrations with a given fibre? We address this question in the context of rational homotopy theory. We construct an infinite family of finite complexes realized (up to rational homotopy) as classifying spaces. We also give several non-realization results, including the following: the rational homotopy types of and are not realized as the classifying space of any simply connected, rational space with finite-dimensional homotopy groups.
Lupton, Gregory and Smith, Samuel Bruce, "Realizing Spaces as Classifying Spaces" (2016). Mathematics Faculty Publications. 284.
First published in Proceedings of The American Mathematical Society in 2016, published by the American Mathematical Society.