Impossibility of obtaining split links from split links via twistings

2001/04/24 by Makoto Ozawa, Ozawa, Makoto
Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25

paper · pdf · doi:10.48550/arxiv.math/0104218

3 pages

arxiv created 2001/04/24 · arxiv updated 2009/11/30

Abstract

We show that if a split link is obtained from a split link L in S³ by 1/n-Dehn surgery along a trivial knot C, then the link L∪ 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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