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-Voli\'c cosimplicial model for the space of long links with $l$ strings in $\mathbb{R}^N$ . We compute explicitely some Euler-Poincar\'e series associated to the second page of that spectral sequence and deduce exponential growth of their Betti numbers.