Transactions of the American Mathematical Society

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



Graphs of tangles

Author: J. C. Gómez-Larrañaga
Journal: Trans. Amer. Math. Soc. 286 (1984), 817-830
MSC: Primary 57M25; Secondary 57N10
MathSciNet review: 760989
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Abstract: We prove that under necessary conditions a graph of tangles is a prime link. For this we generalize the result that the sum of $ 2$-string prime $ L$-tangles is a prime link. Some applications are found. We explore Property $ {\text{L}}$ for tangles in order to prove primeness of knots.

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Keywords: Graph of tangles, primeness, link, knot, Property $ {\text{L}}$, unknotting number
Article copyright: © Copyright 1984 American Mathematical Society