Massey products in the cohomology of groups with applications to link theory

Abstract

Invariants of links in S 3 {S^3} are developed using a modification of the Massey product of one-dimensional classes in the cohomology of certain groups. The theory yields two types of invariants, invariants which depend upon a collection of meridians, or basing, of a link, and invariants which do not. The invariants, which are independent of the basing, are compared with John Milnor’s μ ¯ \overline \mu -invariants. For two component links, a collection of ostensibly based invariants is shown to be independent of the basing. If the linking number of the components of such a link is zero, the resulting invariants may be equivalent to the Sato-Levine-Cochran invariants.