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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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Why do knot cobordisms result in functoriality with respect to knot homologies so often?
Why do knot cobordisms result in functoriality with respect to knot homologies so often?