Let $i: N\to M$ be an immersion of manifolds. If $\dim M\geq 2\dim N+1$ (or something like that?), does there exist arbitrary small perturbations of $i$ (wrt. some reasonable norm) that are already embeddings?
2026-04-01 18:47:18.1775069238
Avoiding self-intersections of immersed manifolds
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This is right, see for example John Lee's "Introduction to Smooth Manifolds", Theorem 6.11. The main idea is to make (by induction) the given immersion injective on succesively larger sets .