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2018 Spaces Realized and Non-Realized as Dold-Lashof Classifying Spaces
Mohamed Rachid Hilali, Abdelhadi Zaim
J. Geom. Symmetry Phys. 50: 29-56 (2018). DOI: 10.7546/jgsp-50-2018-29-56


Let $X$ be a simply connected CW-complex of finite type. Denote by ${\rm Baut}_{1}(X)$ the Dold-Lashof classifying space of fibrations with fiber $X$. \ This paper is a survey about the problem of realizing Dold-Lashof classifying spaces. We will also present some new results: we show that not all rank-two rational $H$-spaces can be realized as ${\rm Baut}_{1}(X)$ for simply connected, rational elliptic space $X$. Moreover, we construct an infinite family of rational spaces $X,$ such that ${\rm Baut}_{1}(X)$ is rationally a finite $H$-space of rank-two (up to rational homotopy type).


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Mohamed Rachid Hilali. Abdelhadi Zaim. "Spaces Realized and Non-Realized as Dold-Lashof Classifying Spaces." J. Geom. Symmetry Phys. 50 29 - 56, 2018.


Published: 2018
First available in Project Euclid: 26 January 2019

zbMATH: 07063859
MathSciNet: MR3929484
Digital Object Identifier: 10.7546/jgsp-50-2018-29-56

Rights: Copyright © 2018 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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