Graphs of tangles

Gómez-Larrañaga, J. C.

doi:10.1090/S0002-9947-1984-0760989-3

Graphs of tangles
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Trans. Amer. Math. Soc. 286 (1984), 817-830 Request permission

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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