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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.
5
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Knot security (When to trust your life with a knot)
Louis Kauffman's masterful book "Knots and Physics" has some thoughts on it. Especially the introductory chapter, and then later a small chapter called "The Theory of Hitches". Worth a reading IMO..
6
votes
2
answers
1k
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Computational complexity of Knot polynomials
What's known about computational complexity of different types of knot invariant polynomials?
For example, Evaluating Jones Polynomial is known to be #P hard.
Is there any reference that surveys such …
20
votes
3
answers
2k
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On connection between Knot theory and Operator algebra
What exactly is the connection between knots and operator algebra? I heard that Jones established such a connection while discovering the celebrated Jones Polynomial.
Now Jones Polynomial is probabl …