Iterated integrals, intersection theory and link groups (Q1059898)

Let L be a smooth link of \(S^ n\), \(\pi =\pi_ 1(S^ 3-L)\) and \(\pi =\Gamma^ 1\supset \Gamma^ 2...\supset \Gamma^ n\supset..\). the lower central series of \(\pi\). (The importance of the lower central series of a link group is that it is an isotropy and cobordism invariant of the link while \(\pi\) itself is not.) Using a recent result of \textit{J. P. Labute} [Trans. Am. Math. Soc. 288, 51-57 (1985)], and \textit{K. T. Chen}'s iterated integrals and formal connections [Bull. Am. Math. Soc. 83, 831-879 (1977; Zbl 0389.58001)] the author gives a presentation of each of the groups \(\pi /\Gamma^ s\) when \(s\geq 2\). The presentation of \(\pi /\Gamma^ s\) is computed from a ''defining system of order s for L'', a family of disks and intervals in \(S^ 3\) whose intersection yields the desired presentation. Many interesting examples illustrate the text.