On the classification of links up to finite type

Nathan Habegger (1) , Jean-Baptiste Meilhan (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 IF - Institut Fourier

We use an action, of 2l-component string links on l-component string links, defined by the first author and Xiao-Song Lin, to lift the indeterminacy of finite type link invariants. The set of links up to this new indeterminacy is in bijection with the orbit space of the restriction of this action to the stabilizer of the identity. Structure theorems for the sets of links up to C_n-equivalence and Self-C_n-equivalence are also given.

Domaines: Topologie géométrique [math.GT]

Nathan Habegger, Jean-Baptiste Meilhan. On the classification of links up to finite type. Topology and physics, 12, World scientific Publishing, pp.138-150, 2008, Nankai Tracts in Mathematics. ⟨hal-00347808⟩