JournalsqtVol. 11, No. 2pp. 323–378

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

  • Eugene Gorsky

    University of California, Davis, USA and National Research University Higher School of Economics, Moscow, Russia
  • Beibei Liu

    Max-Planck-Institut für Mathematik, Bonn, Germany
  • Allison H. Moore

    Virginia Commonwealth University, Richmond, USA
Surgery on links of linking number zero and the Heegaard Floer $d$-invariant cover
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Abstract

We study Heegaard Floer homology and various related invariants (such as the hh-function) for two-component L-space links with linking number zero. For such links, we explicitly describe the relationship between the hh-function, the Sato–Levine invariant and the Casson invariant. We give a formula for the Heegaard Floer dd-invariants of integral surgeries on two-component L-space links of linking number zero in terms of the hh-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+\nu^{+}-invariants of the knots obtained from blowing down the components.

We give a proof of a skein inequality for the dd-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 hh-function, expanding on previous work of the second author, and use these bounds to calculate the four-genus in several examples of links.

Cite this article

Eugene Gorsky, Beibei Liu, Allison H. Moore, Surgery on links of linking number zero and the Heegaard Floer dd-invariant. Quantum Topol. 11 (2020), no. 2, pp. 323–378

DOI 10.4171/QT/137