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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 votes

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..
Arnab's user avatar
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6 votes
2 answers
1k views

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 …
Arnab's user avatar
  • 615
20 votes
3 answers
2k views

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 …
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