Euler series, Stirling numbers and the growth of the homology of the space of long links

Abstract

We study the Bousfield-Kan spectral sequence associated to the Munson-Volić cosimplicial model for the space of long links with $\ell$ strings in $\mathbb R^N$. We compute explicitly some Euler-Poincaré series associated to the second page of that spectral sequence and deduce exponential growth of their Betti numbers.