in your opinion is it possible to get the existence of a tubular neighborhood for a manifold M even if it not embeds smoothly (but only topologically) in some R^N? Thank you!
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5No, consider a "wild knot". Or the Alexander Horned Sphere. – Ryan Budney Oct 24 '13 at 11:52
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Or the sine curve – Oct 24 '13 at 13:25
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Counterexamples mentioned in comments:
- Wild knot, obtained by connecting the endpoints of Fox-Artin arc. This is a topological embedding of $S^1$ into $\mathbb R^3$ without a tubular neighborhood.
- Alexander's horned sphere.
For more, look up wild embeddings.
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