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We show that if a split link is obtained from a split link $L$ in $S^3$ by$1/n$-Dehn surgery along a trivial knot $C$, then the link $L\cup C$ issplittable. That is to say, it is impossible to obtain a split link from asplit link via a non-trivial twisting. As its corollary, we completelydetermine when a trivial link is obtained from a trivial link via a twisting.

IMPOSSIBILITY OF OBTAINING SPLIT LINKS FROM SPLIT LINKS VIA TWISTINGS