Finite type link invariants and the non-invertibility of links

Abstract

We show that a variation of Milnor's $\barμ$-invariants, the so-called Campbell-Hausdorff invariants introduced recently by Stefan Papadima, are of finite type with respect to {\it marked singular links}. These link invariants are stronger than quantum invariants in the sense that they detect easily the non-invertibility of links with more than one components. It is still open whether some effectively computable knot invariants, e.g. finite type knot invariants (Vassiliev invariants), could detect the non-invertibility of knots.

18 pages, amslatex; This is the version to appear in Math. Res. Letters