Milnor invariants and the HOMFLYPT polynomial

Details Milnor invariants and the HOMFLYPT polynomial Milnor invariants and the HOMFLYPT polynomial

2010-02-09

arxiv.org/abs/1002.1803v2

Mathematics

Geometric Topology

Entirely revised version (20 pages). The main result was generalized and extended to Milnor invariants of links, using new arg

Scientific paper

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 \bar{\mu}_J(L) vanishes for any sequence J with length at most k, then any Milnor \bar{\mu}-invariant \bar{\mu}_I(L) 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 non vanishing' Milnor invariants can be always represented as such a linear combination.

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