Geodesic
An example of a fiber in fibrations whose Serre spectral sequences collapse
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 997-1001

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We give an example of a space $X$ with the property that every orientable fibration with the fiber $X$ is rationally totally non-cohomologous to zero, while there exists a nontrivial derivation of the rational cohomology of $X$ of negative degree.
Classification : 55P62, 55R05, 55T10
Keywords: Sullivan minimal model; orientable fibration; TNCZ; negative derivation 
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     author = {Yamaguchi, Toshihiro},
     title = {An example of a fiber in fibrations whose {Serre} spectral sequences collapse},
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Yamaguchi, Toshihiro. An example of a fiber in fibrations whose Serre spectral sequences collapse. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 997-1001. http://geodesic.mathdoc.fr/item/CMJ_2005__55_4_a15/