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Realizing spaces as classifying spaces


Authors: Gregory Lupton and Samuel Bruce Smith
Journal: Proc. Amer. Math. Soc. 144 (2016), 3619-3633
MSC (2010): Primary 55P62, 55R15; Secondary 55P10
Published electronically: January 27, 2016
MathSciNet review: 3503731
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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 $ \mathbb{C} P^2$ and $ S^4$ are not realized as the classifying space of any simply connected, rational space with finite-dimensional homotopy groups.


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Additional Information

Gregory Lupton
Affiliation: Department of Mathematics, Cleveland State University, Cleveland Ohio 44115
Email: G.Lupton@csuohio.edu

Samuel Bruce Smith
Affiliation: Department of Mathematics, Saint Joseph’s University, Philadelphia, Pennsylvania 19131
Email: smith@sju.edu

DOI: https://doi.org/10.1090/proc/13022
Keywords: Classifying space for fibrations, rational homotopy type, derivations, minimal model, finite H-space
Received by editor(s): February 19, 2015
Received by editor(s) in revised form: September 28, 2015
Published electronically: January 27, 2016
Additional Notes: This work was partially supported by a grant from the Simons Foundation (#209575 to the first author). The research was also supported through the program “Research in Pairs” by the Mathematisches Forschungsinstitut Oberwolfach in 2014
Communicated by: Michael A. Mandell
Article copyright: © Copyright 2016 American Mathematical Society