Primeness and sums of tangles

Eudave Muñoz, Mario

doi:10.1090/S0002-9947-1988-0933317-1

Primeness and sums of tangles
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Trans. Amer. Math. Soc. 306 (1988), 773-790 Request permission

Abstract:

We consider knots and links obtained by summing a rational tangle and a prime tangle. For a given prime tangle, we show that there are at most three rational tangles that will induce a composite or splittable link. In fact, we show that there is at most one rational tangle that will give a splittable link. These results extend Scharlemann’s work.

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