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Knot theory is dealing with embedding of curves in manifolds of dimension 3. A knot is a single circle embedded in the affine space of dimension 3 as a smooth curve not crossing itself. Many knot invariants are known and can be used to distinguish knots.
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embedding a circle in S3 [closed]
this is a question that came up in my grad knot theory class. my grad class professor raised the question of circles that can be embedded in S3, and he gave us an example by saying the subset {(x, y) …