WHEN IS THE CLASSIFYING SPACE FOR ELLIPTIC FIBRATIONS RANK ONE?

Abstract

We give a necessary and sufficient condition of a rationally elliptic space X such that the Dold-Lashof classifying space Baut1X for fibrations with the fiber X is rank one. It is only when X has the rational homotopy type of a sphere or the total space of a spherical fibration over a product of spheres.

Keywords

• elliptic space;
• minimal model;
• derivation;
• classifying space for fibrations

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References

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1. Rational cohomologies of classifying spaces for homogeneous spaces of small rank vol.5, pp.4, 2016, https://doi.org/10.1007/s40065-016-0156-y
2. Sullivan minimal models of classifying spaces for non-formal spaces of small rank vol.196, 2015, https://doi.org/10.1016/j.topol.2015.10.003