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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.

4 votes

Is there any genus one knot other than $5_2$ with Alexander polynomial $2t^2-3t+2$?

I finally joined MO this evening to ask an entirely unrelated question, but I thought I might respond to this one as well. The Alexander polynomial does not detect $5_2$, as noted in the previous answ …
John Baldwin's user avatar