The Cochran sequences of semi-boundary links (Q805009)

A 2-component link L is semiboundary if it has linking number 0. Such links have Sato-Levine invariants \(\beta (L)\in \pi_ 3(S^ 2)\cong {\mathbb{Z}}\). The derived link D(L) of \textit{T. D. Cochran} [Comment. Math. Helv. 60, 291-311 (1985; Zbl 0574.57008)] is again semiboundary and so there is a sequence of higher Sato-Levine invariants \(\beta_ i(L)=\beta (D^{i-1}(L))\). The main result of this paper is that such a sequence must satisfy a linear recurrence relation and conversely any linear recurrence sequence is realized by some semiboundary link.