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#### Surgery on links of linking number zero and the Heegaard Floer d-invariant

##### MPS-Authors
/persons/resource/persons249907

Liu,  Beibei
Max Planck Institute for Mathematics, Max Planck Society;

##### External Resource

https://doi.org/10.4171/QT/137
(Publisher version)

##### Fulltext (public)

arXiv:1810.10178.pdf
(Preprint), 698KB

##### Supplementary Material (public)
There is no public supplementary material available
##### Citation

Gorsky, E., Liu, B., & Moore, A. H. (2020). Surgery on links of linking number zero and the Heegaard Floer d-invariant. Quantum Topology, 11(2), 323-378. doi:10.4171/QT/137.

Cite as: http://hdl.handle.net/21.11116/0000-0006-D973-4
##### Abstract
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 $\nu^{+}$-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.