Abstract
To each simply connected topological space is associated a graded Lie algebra; the rational homotopy Lie algebra. The Avramov-Felix conjecture says that for a space of finite Ljusternik-Schnirelmann category this Lie algebra contains a free Lie subalgebra on two generators. We prove the conjecture in the case when the Lie algebra has depth one.
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Bøgvad, R., Jacobsson, C. Graded lie algebras of depth one. Manuscripta Math 66, 153–159 (1990). https://doi.org/10.1007/BF02568488
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DOI: https://doi.org/10.1007/BF02568488