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I had asked this question on math.stackexchange 2 days back but came up empty handed so I wanted to ask it here. Are there known examples of $2$ non equivalent knots that have identical jones ...

Let $L_1$ and $L_2$ be two nonintersecting picewise-linear or smooth knots in $\mathbb R^3$. Suppose they are ambient isotopic. Does there exist an embedded surface $f: S^1\times[0,1]\to \mathbb R^3$ ...