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Oct 28, 2017 at 13:29 vote accept Mohammed Sabak
Oct 27, 2017 at 14:59 answer added Bruno Martelli timeline score: 2
Oct 26, 2017 at 20:48 comment added Nick L Maybe you want to add the condition something like $\partial D_{K}$ and $\partial D_{K}'$ are in the same class in the fundamental group of the link complement. Otherwise it is clearly false, take one Disk that does not change the link (say it only intersects $L_{1}$ in one point), and one where the operation is non-trivial, such as your example above.
Oct 26, 2017 at 19:58 history edited Mohammed Sabak
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Oct 26, 2017 at 19:12 history asked Mohammed Sabak CC BY-SA 3.0