New link invariants and applications (Q1098457)

This paper provides a sequence of invariants for codimension two links, which vanish on boundary links and are invariant under link cobordism. The components of a link L are not required to be spheres, but the main theorem of the paper, in which the invariants and their properties are stated, has \(H_ 1(L)=0\) as part of its hypothesis. The invariants are based on the lower central series of the link group, and as the author points out, should be compared to the classical link cobordism invariants of J. Milnor. The new invariants are related to the Sato-Levine invariant \(\beta\) (L), which is shown to vanish if either \(H_ 1(L)=0\), or if L has at least four components (and \(\beta\) (L) is defined). \textit{T. D. Cochran} has shown that almost all of these new invariants vanish when L is a spherical link, that is, when each component is a sphere [Invent. Math. 90, 635-645 (1987; Zbl 0637.57015), see the review above].