Characterization of Finite Type String Link Invariants of Degree < 5

Abstract

In this paper, 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 closure of (cabled) string links. We show that finite type invariants classify string links up to C_k-moves for k<6, which proves, at low degree, a conjecture due to Goussarov and Habiro. We also give a similar characterization of finite type concordance invariants of degree <6.

References in corpus (1)

• Finite-type invariants of three-manifolds and the dimension subgroup problem

Cited by in corpus (7)

• Arrow calculus for welded and classical links
• Whitney tower concordance of classical links
• Classification of string links up to $2n$-moves and link-homotopy
• Abelian quotients of the string link monoid
• Clasper Concordance, Whitney towers and repeating Milnor invariants
• Self $C_2$-equivalence of two-component links and invariants of link maps
• On finite type invariants of welded string links and ribbon tubes