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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Primeness and sums of tangles


Author: Mario Eudave Muñoz
Journal: Trans. Amer. Math. Soc. 306 (1988), 773-790
MSC: Primary 57M25
MathSciNet review: 933317
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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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DOI: https://doi.org/10.1090/S0002-9947-1988-0933317-1
Keywords: Prime tangle, rational tangle, prime knot and link, composite knot and link, splittable link
Article copyright: © Copyright 1988 American Mathematical Society