We give formulas expressing Milnor invariants of an n-component link L in the 3-sphere in terms of the HOMFLYPT polynomial as follows. If the Milnor invariant ̄μL(J) vanishes for any sequence J with length at most k, then any Milnor ̄μ-invariant ̄μL(I) with length between 3 and 2k + 1 can be represented as a combination of HOMFLYPT polynomial of knots obtained from the link by certain band sum operations. In particular, the first nonvanishing Milnor invariants can be always represented as such a linear combination.
ASJC Scopus subject areas
- Geometry and Topology