Characterization of finite type string link invariants of degree < 5

Jean-Baptiste Meilhan (1) , Akira Yasuhara (2)

1 IF - Institut Fourier
2 Tokyo Gakugei University

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.

Domaines: Topologie géométrique [math.GT]

Jean-Baptiste Meilhan, Akira Yasuhara. Characterization of finite type string link invariants of degree < 5. Mathematical Proceedings of the Cambridge Philosophical Society, 2010, 148, pp.439-472. ⟨hal-00374875⟩