2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138290We show that the Bousfield-Kan spectral sequence which computes the rational homotopy groups of the space of long knots in ${\mathbb R}^d$, where $d\ge 4$, collapses at the $E^2$ page. The main ingredients in the proof are Sinha's cosimplicial model for the space of long knots and a coformality result for the little balls operad.12 pages. Revised (and presumably final) version. Accepted for publication in Mathematical Research LettersAlgebraic Topology57Q45text