2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60277We give the first explicit computations of rational homotopy groups of spaces of "long knots" in Euclidean spaces. We define a spectral sequence which converges to these rational homotopy groups whose E^1 term is defined in terms of braid Lie algebras. For odd k we establish a vanishing line for this spectral sequence, show the Euler characteristic of the rows of this E^1 term is zero, and make calculations of E^2 in a finite range.11 pagesAlgebraic TopologyGeometric TopologyQuantum Algebra57R40text