VASSILIEV HOMOTOPY STRING LINK INVARIANTS

DROR BAR-NATAN
1995 Journal of knot theory and its ramifications  
We investigate Vassiliev homotopy invariants of string links, and find that in this particular case, most of the questions left unanswered in [3] can be answered affirmatively. In particular, Vassiliev invariants classify string links up to homotopy, and all Vassiliev homotopy string link invariants come from marked surfaces as in [3], using the same construction that in the case of knots gives the HOMFLY and Kauffman polynomials. Alongside, the Milnor µ invariants of string links are shown to
more » ... e Vassiliev invariants, and it is re-proven, by elementary means, that Vassiliev invariants classify braids.
doi:10.1142/s021821659500003x fatcat:pa7cmyyj7zdupbvl72cdpp3hs4