Asymptotic Massey products, induced currents and Borromean torus links

Abstract

We introduce a class of currents which allows a new and very explicit form for the Massey product of a third order link as a line integral. The explicit form permits the introduction of an asymptotic Massey product analogous to that introduced previously for Gauss’s integral by V. Arnold. The average third order asymptotic Massey product is shown to be equal to Berger’s third order helicity for divergence-free vector fields in linked tori.