Analytic properties of Poincaré series of spaces
Let \(X\) be a finite simply connected CW-complex such that its rational homotopy groups are non trivial in infinitely many dimensions. Under certain conditions, the author claims that the sum \[ \sum^{k+\dim X-1}_{k+1}\text{ rank} \pi_j(\Omega X)k\omega^k \] is bounded between two constants, where \(\omega\) is the radius of convergence of the Poincaré series with \(\omega<1\).
scientific article; zbMATH DE number 1307809