Characterization of finite type string link invariants of degree <5

Abstract

AbstractWe give a complete set of finite type string link invariants of degree <5. In addition to Milnor invariants, these include several string link invariants constructed by evaluating knot invariants on certain closures of (cabled) string links. We show that finite type invariants classify string links up toCk-moves fork≤ 5, which proves, at low degree, a conjecture due to Goussarov and Habiro. We also give a similar classification of string links up toCk-moves and concordance fork≤ 6.