Immersed concordances of links and Heegaard Floer homology

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 $\delta$-constant deformations of singularities with many branches.

35 pages, 7 figures

References in corpus (5)

• Floer homology and knot complements
• Floer Simple Manifolds and L-Space Intervals
• A note on cobordisms of algebraic knots
• Unlinking information from 4-manifolds
• Blanchfield forms and Gordian distance

Cited by in corpus (5)

• Four genera of links and Heegaard Floer homology
• Fibered and strongly quasi-positive $L$-space links
• L-space surgeries on 2-component L-space links
• Four manifolds with no smooth spines
• Splitting numbers and signatures