Characterization of Finite Type String Link Invariants of Degree < 5

TL;DR

This paper provides a complete classification of finite type string link invariants of degree less than 5, expanding understanding of their structure and relation to knot invariants, and confirming a conjecture for low degrees.

Contribution

It introduces a comprehensive set of invariants for string links of degree <5, including new constructions, and proves classification up to certain moves, confirming a conjecture in the field.

Findings

Finite type invariants classify string links up to C_k-moves for k<6.

Includes new invariants derived from knot invariants on closures.

Confirms a conjecture by Goussarov and Habiro for low degrees.

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.