  We determine the quantum filtration structure of the Lee homology of all
torus links. In particular, this determines the $s$-invariant of a torus link
equipped with any orientation. In the special case $T(n,n)$, our result
confirms a conjecture of Pardon, as well as a conjecture of
Manolescu-Marengon-Sarkar-Willis which establishes an adjunction-type
inequality of the $s$-invariant for cobordisms in $k\overline{\mathbb{CP}^2}$.
We also give a few applications of this adjunction inequality.
