Impossibility of obtaining split links from split links via twistings

Details Impossibility of obtaining split links from split links via twistings Impossibility of obtaining split links from split links via twistings

2001-04-24

arxiv.org/abs/math/0104218v1

Mathematics

Geometric Topology

3 pages

Scientific paper

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 $L\cup C$ is
splittable. That is to say, it is impossible to obtain a split link from a
split link via a non-trivial twisting. As its corollary, we completely
determine when a trivial link is obtained from a trivial link via a twisting.

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