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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.

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https://hal.archives-ouvertes.fr/hal-01392100
Contributor : Okina Université d'Angers <>
Submitted on : Friday, November 4, 2016 - 10:10:23 AM
Last modification on : Monday, March 9, 2020 - 6:15:54 PM

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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. ⟨10.1016/j.jpaa.2014.05.008⟩. ⟨hal-01392100⟩

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