Lee filtration structure of torus links

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 kCP 2 .We also give a few applications of this adjunction inequality.