= 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>.
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