Realizing spaces as classifying spaces

Gregory M Lupton; Samuel Bruce Smith

doi:10.1090/proc/13022

Realizing spaces as classifying spaces

Gregory M Lupton
, Samuel Bruce Smith

Saint Joseph’s University

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English
Pages (from-to)	3619-3633
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	144
Issue number	8
DOIs	https://doi.org/10.1090/proc/13022
State	Published - Jan 1 2016

Keywords

Classifying space for fibrations
Derivations
Finite H-space
Minimal model
Rational homotopy type

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AB - 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.

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KW - Finite H-space

KW - Minimal model

KW - Rational homotopy type

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Realizing spaces as classifying spaces

Abstract

Keywords

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