The ranks of the homotopy groups of odd degree of a finite complex

Abstract :

Let L be a graded connected Lie algebra of finite type and finite depth (for instance the rational homotopy Lie algebra of a finite simply connected CW complex). Let L ( p ) = { L p k } k ≥ 1 . Then for any prime p, lim n ⁡ log ⁡ dim ⁡ L ( p ) ≤ n log ⁡ dim ⁡ L ≤ n = 1 . In particular for a space X, the Lie algebra L X = π ⁎ ( Ω X ) ⊗ Q and its even dimensional part L X ( 2 ) have the same log index.

Type de document :
Article dans une revue
Journal of Pure and Applied Algebra, Elsevier, 2015, 219 (3), pp.494-501. 〈http://linkinghub.elsevier.com/retrieve/pii/S0022404914001157〉. 〈10.1016/j.jpaa.2014.05.008〉
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https://hal.archives-ouvertes.fr/hal-01392100
Contributeur : Okina Université d'Angers <>
Soumis le : vendredi 4 novembre 2016 - 10:10:23
Dernière modification le : lundi 5 février 2018 - 15:00:03

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Yves Felix, Steve Halperin, Jean-Claude Thomas. The ranks of the homotopy groups of odd degree of a finite complex. Journal of Pure and Applied Algebra, Elsevier, 2015, 219 (3), pp.494-501. 〈http://linkinghub.elsevier.com/retrieve/pii/S0022404914001157〉. 〈10.1016/j.jpaa.2014.05.008〉. 〈hal-01392100〉

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