Characterization of finite type string link invariants of degree <5

Abstract

Abstract We 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 to C k -moves for k ≤ 5, which proves, at low degree, a conjecture due to Goussarov and Habiro. We also give a similar classification of string links up to C k -moves and concordance for k ≤ 6.