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Full-Text Articles in Physical Sciences and Mathematics
Realizing Spaces As Classifying Spaces, Gregory Lupton, Samuel Bruce Smith
Realizing Spaces As Classifying Spaces, Gregory Lupton, Samuel Bruce Smith
Mathematics and Statistics Faculty Publications
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.