COMBINATORIC MASSEY–MILNOR LINKING THEORY

In this paper following the scheme of Massey–Milnor invariant theory [C. C. Hsieh, Combinatoric and diagrammatic studies in knot theory J. Knot Theory Ramifications16 (2007) 1235–1253; C. C. Hsieh, Massey-Milnor linking = Chern-Simons-Witten graphs, J. Knot Theory Ramifications17 (2008) 877–903; C. C. Hsieh and S. W. Yang, Chern-Simons-Witten configuration space integrals in knot theory, J. Knot Theory Ramifications14 (2005) 689–711], we studied the first non-vanishing linkings of knot theory in ℝ3 and also derived the combinatorial formulae from which we could read out the invariants directly from the knot diagrams. Though the theme is calculus, the idea comes from perturbative quantum field theory.

THE TOPOLOGICAL THEORY OF THE MILNOR INVARIANT $\bar\mu(1,2,3)$

We study a topological Abelian gauge theory that generalizes the Abelian Chern–Simons one, and that leads in a natural way to the Milnor's link invariant [Formula: see text] when the classical action on-shell is calculated.