# Rational homotopy of Serre fibrations

Annales de l'institut Fourier (1981)

- Volume: 31, Issue: 3, page 71-90
- ISSN: 0373-0956

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topThomas, Jean-Claude. "Rational homotopy of Serre fibrations." Annales de l'institut Fourier 31.3 (1981): 71-90. <http://eudml.org/doc/74508>.

@article{Thomas1981,

abstract = {In rational homotopy theory, we show how the homotopy notion of pure fibration arises in a natural way. It can be proved that some fibrations, with homogeneous spaces as fibre are pure fibrations. Consequences of these results on the operation of a Lie group and the existence of Serre fibrations are given. We also examine various measures of rational triviality for a fibration and compare them with and whithout the hypothesis of pure fibration.},

author = {Thomas, Jean-Claude},

journal = {Annales de l'institut Fourier},

keywords = {rational homotopy theory; pure fibration; fibrations with homogeneous spaces as fibre; existence of Serre fibrations; rational triviality for a fibration; minimal model},

language = {eng},

number = {3},

pages = {71-90},

publisher = {Association des Annales de l'Institut Fourier},

title = {Rational homotopy of Serre fibrations},

url = {http://eudml.org/doc/74508},

volume = {31},

year = {1981},

}

TY - JOUR

AU - Thomas, Jean-Claude

TI - Rational homotopy of Serre fibrations

JO - Annales de l'institut Fourier

PY - 1981

PB - Association des Annales de l'Institut Fourier

VL - 31

IS - 3

SP - 71

EP - 90

AB - In rational homotopy theory, we show how the homotopy notion of pure fibration arises in a natural way. It can be proved that some fibrations, with homogeneous spaces as fibre are pure fibrations. Consequences of these results on the operation of a Lie group and the existence of Serre fibrations are given. We also examine various measures of rational triviality for a fibration and compare them with and whithout the hypothesis of pure fibration.

LA - eng

KW - rational homotopy theory; pure fibration; fibrations with homogeneous spaces as fibre; existence of Serre fibrations; rational triviality for a fibration; minimal model

UR - http://eudml.org/doc/74508

ER -

## References

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- [10] S. HALPERIN, Finiteness in the minimal model of Sullivan, Trans. of the A.M.S., vol. 230 (1977), 173-199. Zbl0364.55014MR57 #1493
- [11] S. HALPERIN and J. STASHEFF, Obstruction to homotopy equivalences, Advances in Math., 32 (1979), 233-279. Zbl0408.55009MR80j:55016
- [12] J.L. KOSZUL, Homologie et cohomologie des algèbres de Lie, Bull. S.M.F., 78 (1950). Zbl0039.02901MR12,120g
- [13] J.M. LEMAIRE, "Autopsie d'un meurtre"..., Ann. Sc. E.N.S. 4ème série, t. 1.1 (1978), 93-100. Zbl0382.55011MR58 #18423
- [14] J. NEISENDORFER, Formal and coformal spaces, Illinois Journal of Mathematics, vol. 22, Number 4 (1978), 565-580. Zbl0396.55011MR58 #18429
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- [17] J.C. THOMAS, Homotopie rationnelle des fibrés de Serre, Thèse Université de Lille I (1980) et C.R.A.S., n° 290 (1980), 811-813.

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