Realizing spaces as classifying spaces
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- by Gregory Lupton and Samuel Bruce Smith PDF
- Proc. Amer. Math. Soc. 144 (2016), 3619-3633 Request permission
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.References
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Additional Information
- Gregory Lupton
- Affiliation: Department of Mathematics, Cleveland State University, Cleveland Ohio 44115
- MR Author ID: 259990
- Email: G.Lupton@csuohio.edu
- Samuel Bruce Smith
- Affiliation: Department of Mathematics, Saint Joseph’s University, Philadelphia, Pennsylvania 19131
- MR Author ID: 333158
- Email: smith@sju.edu
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3619-3633
- MSC (2010): Primary 55P62, 55R15; Secondary 55P10
- DOI: https://doi.org/10.1090/proc/13022
- MathSciNet review: 3503731