Realizing spaces as classifying spaces

2015/02/19 by Gregory Lupton, Lupton, Gregory, Samuel Bruce Smith +1
Mathematics · #55P62 #55R15 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:55P62 #msc:55R15

paper · pdf · doi:10.48550/arxiv.1502.05625

14 pages

arxiv created 2015/02/19 · arxiv updated 2015/02/20

Abstract

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 ℂP² and S⁴ are not realized as the classifying space of any simply connected, rational space with finite-dimensional homotopy groups.

Related

• Fibrations of classifying spaces in the simplicial setting
• Algebraic models for classifying spaces of fibrations
• Rational Homotopy Type of the Classifying Space for Fibrewise Self-Equivalences
• The universal fibration with fibre X in rational homotopy theory
• Sullivan minimal models of classifying spaces for non-formal spaces of small rank