Characterization of Finite Type String Link Invariants of Degree < 5

Details Characterization of Finite Type String Link Invariants of Degree < 5 Characterization of Finite Type String Link Invariants of Degree < 5

2009-04-09

arxiv.org/abs/0904.1527v1

Math. Proc. Camb. Phil. Soc. 148 (2010), 439-472

Mathematics

Geometric Topology

Scientific paper

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.

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