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.
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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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/

[1] I. Belegradek and V.  Kapovitch: Obstructions to nonnegative curvature and rational homotopy theory. J. Amer. Math. Soc. 16 (2003), 259–284. | MR

[2] Y. Félix, S. Halperin and J. C. Thomas: Rational Homotopy Theory. Springer GTM, 205, New York, 2001. | MR

[3] S.  Halperin: Rational fibrations, minimal models, and fibrings of homogeneous spaces. Trans.  A.M.S. 244 (1978), 199–244. | DOI | MR | Zbl

[4] M. Markl: Towards one conjecture on collapsing of the Serre spectral sequence. Rend. Circ. Mat. Palermo (2) Suppl. 22 (1990), 151–159. | MR | Zbl

[5] W.  Meier: Rational universal fibrations and flag manifolds. Math. Ann. 258 (1982), 329–340. | DOI | MR | Zbl

[6] M. Schlessinger and J.  Stasheff: Deformation theory and rational homotopy type. Preprint.

[7] D.  Sullivan: Infinitesimal computations in topology. Publ.  I.H.E.S. 47 (1977), 269–331. | DOI | MR | Zbl