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

<p>Special Issue in honor of Prof. Hans-Bjørn Foxby</p>

International audience

<p>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.</p>