Immersed concordance of links and Heegaard Floer homology

An immersed concordance between two links is a concordance with possible-intersections. Given an immersed concordance we construct a smooth-dimensional cobordism between surgeries on links. By applying-invariant inequalities for this cobordism we obtain inequalities between H-functions of links, which can be extracted from the link Floer homology. As an application we show a Heegaard Floer theoretical criterion for the splitting number of links. The criterion is especially effective L-space links, and we present an infinite family of L-space links with linking numbers and arbitrary large splitting numbers. We also show a of the H-function under \δ-constant deformations of with many branches.