Lee filtration structure of torus links, adjunction inequality, and applications

We state our recent result determining the quantum filtration structure of the Lee homology of torus links. This implies a relative adjunction-type inequality for s-invariants of two links related by a link cobordism in kCP^2, originally conjectured by Manolescu-Marengon-Sarkar-Willis. As applications of this inequality, we show the existence of knots with arbitrarily large CP^2 genus, and we explain why the inequality might be useful for constructing exotic kCP^2's.