We study Heegaard Floer homology and various related invariants (such as the h-function) for two-component L-space links with linking number zero. For such links, we explicitly describe the relationship between the h-function, the Sato-Levine invariant and the Casson invariant. We give a formula for the Heegaard Floer d-invariants of integral surgeries on two-component L-space links of linking number zero in terms of the h-function, generalizing a formula of Ni and Wu. As a consequence, for such links with unknotted components, we characterize L-space surgery slopes in terms of the ν + -invariants of the knots obtained from blowing down the components.We give a proof of a skein inequality for the d-invariants of +1 surgeries along linking number zero links that differ by a crossing change. We also describe bounds on the smooth four-genus of links in terms of the h-function, expanding on previous work of the second author, and use these bounds to calculate the four-genus in several examples of links.

We establish some new relationships between Milnor invariants and Heegaard Floer homology. This includes a formula for the Milnor triple linking number from the link Floer complex, detection results for the Whitehead link and Borromean rings, and a structural property of the d-invariants of surgeries on certain algebraically split links.