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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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Can you characterize the group of transformations of knot diagrams which preserve the knot e...
Suppose we call a knot an equivalence class of embeddings of S1 --> R3 under ambient isotopy, a knot representative a particular such embedding, and a knot diagram the "2 1/2 dimensional" shadow of su …