Sur Les Groupes D’Homotopie Des Espaces Dont La Cohomologie Modulo 2 Est Nilpotente |
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Authors: | Jean Lannes Lionel Schwartz |
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Affiliation: | (1) Ecole Polytechnique, Centre de Mathématiques, UA 169 du CNRS, route de Saclay, F-91128 Palaiseau, Cedex, France;(2) Université de Paris-Sud, Mathématiques, Bat 425, UA 11 69 du CNRS, F-91405 Orsay, Cedex, France |
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Abstract: | The main object of this note is to prove the following generalisation of a theorem of Serre. A simply connected space of finite type whose mod. 2 cohomology is nilpotent (and non-trivial) has infinitely many homotopy groups which are not of odd torsion. Incidentally we show that for every fibrationF( → ί )E ( → p )B, satisfying certain mild conditions, the following holds. If a classx in the mod. 2 cohomology ofE belongs to the kernel ofi*, then some power ofx belongs to the ideal generated by the image underp* of the mod. 2 reduced cohomology ofB. |
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