分野別セミナー

（joint work with Jean-Baptiste Meilhan (Univ of Grenoble I)）
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.