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Heegaard Floer correction terms of 1-surgeries along (2, q)-cablings Sato, Kouki


The Heegaard Floer correction term (d-invariant) is an invariant of rational homology 3-spheres equipped with a \(\mbox{Spin}^c\) structure. In particular, the correction term of 1-surgeries along knots in the 3-sphere is a (2Z-valued) knot concordance invariant d1. In this work, we estimate d1 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. By using this estimate, we obtain two corollaries. One of the corollaries shows that the relationship between d1 and the Heegaard Floer tau invariant is very weak in general. The other one gives infinitely many knots which cannot be unknotted either by only positive crossing changes or by only negative crossing changes.

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