The Self-Intersections of a Smooth n-Manifold in 2n-Space¶
Whitney, H. (1944). The Self-Intersections of a Smooth n-Manifold in 2n-Space. Annals of Mathematics, 45(2), 220-246.
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Primes¶
- Embeddability
- Topology contributes manifold embedding — Whitney's theorem that every smooth \(n\)-manifold embeds in \(\mathbb{R}^{2n}\) — and knot theory treats the classification of knots as the classification of conflict-free embeddings of a circle in 3-space under isotopy equivalence.
This sourceProves that the self-intersections of a smooth n-manifold immersed in 2n-space can be removed, yielding the embedding theorem that every smooth n-manifold embeds in ℝ^{2n}.
- Topology contributes manifold embedding — Whitney's theorem that every smooth \(n\)-manifold embeds in \(\mathbb{R}^{2n}\) — and knot theory treats the classification of knots as the classification of conflict-free embeddings of a circle in 3-space under isotopy equivalence.
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