An example of a fiber in fibrations whose Serre spectral sequences collapse

Toshihiro Yamaguchi

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 4, page 997-1001
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Yamaguchi, Toshihiro. "An example of a fiber in fibrations whose Serre spectral sequences collapse." Czechoslovak Mathematical Journal 55.4 (2005): 997-1001. <http://eudml.org/doc/31006>.

@article{Yamaguchi2005,
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.},
author = {Yamaguchi, Toshihiro},
journal = {Czechoslovak Mathematical Journal},
keywords = {Sullivan minimal model; orientable fibration; TNCZ; negative derivation; Sullivan minimal model; orientable fibration; TNCZ; negative derivation},
language = {eng},
number = {4},
pages = {997-1001},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An example of a fiber in fibrations whose Serre spectral sequences collapse},
url = {http://eudml.org/doc/31006},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Yamaguchi, Toshihiro
TI - An example of a fiber in fibrations whose Serre spectral sequences collapse
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 4
SP - 997
EP - 1001
AB - 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.
LA - eng
KW - Sullivan minimal model; orientable fibration; TNCZ; negative derivation; Sullivan minimal model; orientable fibration; TNCZ; negative derivation
UR - http://eudml.org/doc/31006
ER -

References

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  1. Obstructions to nonnegative curvature and rational homotopy theory, J. Amer. Math. Soc. 16 (2003), 259–284. (2003) MR1949160
  2. Rational Homotopy Theory, Springer GTM, 205, New York, 2001. (2001) MR1802847
  3. 10.1090/S0002-9947-1978-0515558-4, Trans.  A.M.S. 244 (1978), 199–244. (1978) Zbl0387.55010MR0515558DOI10.1090/S0002-9947-1978-0515558-4
  4. Towards one conjecture on collapsing of the Serre spectral sequence, Rend. Circ. Mat. Palermo (2) Suppl. 22 (1990), 151–159. (1990) Zbl0705.55007MR1061796
  5. 10.1007/BF01450686, Math. Ann. 258 (1982), 329–340. (1982) Zbl0466.55012MR0649203DOI10.1007/BF01450686
  6. Deformation theory and rational homotopy type, Preprint. 
  7. 10.1007/BF02684341, Publ.  I.H.E.S. 47 (1977), 269–331. (1977) Zbl0374.57002MR0646078DOI10.1007/BF02684341

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