Simple links and tangles (Q788326)

The author introduces the notion of a simple tangle, and shows that a sum of two simple tangles is a simple link. Some practical criteria for a tangle to be simple are given; thus this paper provides an effective method for constructing simple links. As an application, it is shown that a link in \(S^ 3\) is concordant to a simple link with the same Alexander invariant. This sharpens results of \textit{S. A. Bleiler} [Pac. J. Math. 100, 249-257 (1982; Zbl 0519.57003)] and \textit{Y. Nakanishi} [Math. Semin. Notes, Kobe Univ. 8, 561-568 (1980; Zbl 0457.57003)].