Previous |  Up |  Next

Article

Keywords:
Sullivan minimal model; orientable fibration; TNCZ; negative derivation
Summary:
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.
References:
[1] I. Belegradek and V.  Kapovitch: Obstructions to nonnegative curvature and rational homotopy theory. J. Amer. Math. Soc. 16 (2003), 259–284. MR 1949160
[2] Y. Félix, S. Halperin and J. C. Thomas: Rational Homotopy Theory. Springer GTM, 205, New York, 2001. MR 1802847
[3] S.  Halperin: Rational fibrations, minimal models, and fibrings of homogeneous spaces. Trans.  A.M.S. 244 (1978), 199–244. DOI 10.1090/S0002-9947-1978-0515558-4 | MR 0515558 | Zbl 0387.55010
[4] M. Markl: Towards one conjecture on collapsing of the Serre spectral sequence. Rend. Circ. Mat. Palermo (2) Suppl. 22 (1990), 151–159. MR 1061796 | Zbl 0705.55007
[5] W.  Meier: Rational universal fibrations and flag manifolds. Math. Ann. 258 (1982), 329–340. DOI 10.1007/BF01450686 | MR 0649203 | Zbl 0466.55012
[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 10.1007/BF02684341 | MR 0646078 | Zbl 0374.57002
Partner of
EuDML logo