The ranks of the homotopy groups of odd degree of a finite complex - Archive ouverte HAL Access content directly
Journal Articles Journal of Pure and Applied Algebra Year : 2015

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.

No file

Dates and versions

hal-01392100 , version 1 (04-11-2016)

Identifiers

Cite

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, 2015, 219 (3), pp.494-501. ⟨10.1016/j.jpaa.2014.05.008⟩. ⟨hal-01392100⟩
49 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More