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Surgery on links of linking number zero and the Heegaard Floer $d$-invariant
Published Web Location
https://doi.org/10.4171/qt/137Abstract
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 v+-invariants of the knots obtained from blowing down the components. We give a proof of a skein inequality for the d-invariants of C1 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.
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