2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68567We prove that there is no functorial universal finite type invariant for braids in $Σ\times I$ if the genus of $Σ$ is positive.6p., revised version, C.R.Acad.Sci.Paris, to appearGeometric TopologyGroup Theory20F36, 57M27, 57N05, 55P62text