Stavros Garoufalidis and Andrew Kricker.
Abstract: We construct an invariant of boundary links which is at least as strong as the Kontsevich integral, determines the $S$-equivalence class of a boundary link and which takes values in a space of trivalent graphs whose edges are decorated by rational functions in noncommuting variables. Our invariant is axiomatically characterized by a universal property closely related to the Homology Surgery view of boundary links, and comes equipped with a diagrammatic integration theory, in the spirit of perturbative quantum field theory.
Key words: Boundary links, Kontsevich integral, Cohn localization.
Notes: 48 pages, 31 figures.