Immersed concordances of links and Heegaard Floer homology

Maciej Borodzik; Eugene Gorsky

doi:10.1512/iumj.2018.67.7375

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arXiv · 1601.07507

Immersed concordances of links and Heegaard Floer homology

Maciej Borodzik·Eugene Gorsky

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Abstract

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

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BibTeX RIS

Maciej Borodzik, Eugene Gorsky. 2016-01-27. Immersed concordances of links and Heegaard Floer homology. https://doi.org/10.1512/iumj.2018.67.7375

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