Heegaard Floer correction terms of $(+1)$-surgeries along $(2,q)$-cablings

Abstract

The Heegaard Floer correction term ($d$-invariant) is an invariant of rational homology 3-spheres equipped with a Spin${}^c$ structure. In particular, the correction term of 1-surgeries along knots in $S^3$ is a ($2\mathbb{Z}$-valued) knot concordance invariant $d_1$. In this paper, we estimate $d_1$ for the $(2,q)$-cable of any knot $K$. This estimate does not depend on the knot type of $K$. If $K$ belongs to a certain class which contains all negative knots, then equality holds. As a corollary, we show that the relationship between $d_1$ and the Heegaard Floer $\tau$-invariant is very weak in general.

12 pages, 10 figures

References in corpus (3)

• Floer homology and knot complements
• A concordance invariant from the Floer homology of +/- 1 surgeries
• The $E_8$-boundings of homology spheres and negative sphere classes in $E(1)$

Cited by in corpus (1)

• Knots that are not slice either in positons or in negatons