A note on cobordisms of algebraic knots

Abstract

In this note we use Heegaard Floer homology to study smooth cobordisms of algebraic knots and complex deformations of cusp singularities of curves. The main tool will be the concordance invariant ${\nu }^{+}$: we study its behaviour with respect to connected sums, providing an explicit formula in the case of L-space knots and proving subadditivity in general.

17 pages, 5 figures. Improved exposition and organisation, fixed a gap in the proof of Proposition 6.1

References in corpus (2)

• On knot Floer homology and cabling II
• The Upsilon function of L-space knots is a Legendre transform

Cited by in corpus (16)

• Immersed concordances of links and Heegaard Floer homology
• Topologically slice knots that are not smoothly slice in any definite 4-manifold
• On rational sliceness of Miyazaki's fibered, $-$amphicheiral knots
• Genus one cobordisms between torus knots
• The ${\nu }^{+}$-equivalence classes of genus one knots
• A full-twist inequality for the ${\nu }^{+}$-invariant
• Involutive Heegaard Floer homology and rational cuspidal curves
• Census L-space knots are braid positive, except for one that is not
• Knot concordance invariants from Seiberg-Witten theory and slice genus bounds in 4-manifolds
• A note on the four-dimensional clasp number of knots
• New Heegaard Floer slice genus and clasp number bounds
• Truncated Heegaard Floer Homology and Knot Concordance Invariants
• Two curious strongly invertible L-space knots
• On the nonorientable four-ball genus of torus knots
• Links with nontrivial Alexander polynomial which are topologically concordant to the Hopf link
• Knots that are not slice either in positons or in negatons