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The loop space homology $H\\_*(\\Omega X;\\mathbb Q)$ is the universal enveloping algebra of a graded Lie algebra $L\\_X$ isomorphic with $ pi\\_{*-1} (X)\\otimes \\mathbb Q$. Let $Q\\_X \\subset L\\_X$ be a minimal generating subspace, and set $\\alpha = \\limsup\\_i \\frac{\\log{\\scriptsize rk} \\pi\\_i(X)}{i}$. 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