I know Jones' polynomial is a knot invariant. By using knot invariant like p-coloration one can only say whether two knots are different but not whether they are the same. So it is like injective mappings. I was wondering whether more powerful knot invariant exists (which can tell whether two knots are same or not) and is Jones' polynomial one of them?
2026-03-27 23:47:53.1774655273
Is there a one to one correspondence between Jones' polynomials and knots?
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We call invariants that have distinct values for each knot complete. The Jones polynomial is not complete. This is the in book Knot Theory and Its Applications By Kunio Murasugi.
Hope this helps.