 General position for curves in a manifold

Smooth maps of finitely many circles into a manifold of dimension at least three can be perturbed within their homotopy classes to disjoint embeddings. The transversality dimension count for two curve branches is $1+1-m<0$, so their images avoid one another after perturbation; one also removes self-intersections and obtains immersions by the jet version of transversality. This allows disjoint representative loops for relators in high-dimensional surgery constructions of prescribed fundamental groups.