Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. Belegradek and V. Kapovitch: Obstructions to nonnegative curvature and rational homotopy theory. J. Amer. Math. Soc. 16 (2003), 259–284.
Y. Felix, S. Halperin and J. C. Thomas: Rational Homotopy Theory. Springer GTM, 205, New York, 2001.
S. Halperin: Rational fibrations, minimal models, and fibrings of homogeneous spaces. Trans. A.M.S. 244 (1978), 199–244.
M. Markl: Towards one conjecture on collapsing of the Serre spectral sequence. Rend. Circ. Mat. Palermo (2) Suppl. 22 (1990), 151–159.
W. Meier: Rational universal fibrations and flag manifolds. Math. Ann. 258 (1982), 329–340.
M. Schlessinger and J. Stasheff: Deformation theory and rational homotopy type. Preprint.
D. Sullivan: Infinitesimal computations in topology. Publ. I.H.E.S. 47 (1977), 269–331.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yamaguchi, T. An Example of a Fiber in Fibrations Whose Serre Spectral Sequences Collapse. Czech Math J 55, 997–1001 (2005). https://doi.org/10.1007/s10587-005-0083-0
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10587-005-0083-0