Correction to the article Floer homology and splicing knot complements

Abstract

This note corrects the mistakes in the splicing formulas of the paper “Floer homology and splicing knot complements” (Algebr. Geom. Topol. 15 (2015) 3155–3213). The mistakes are the result of the incorrect assumption that for a knot $K$ inside a homology sphere $Y$, the involution on $\widehat{HFK}\left(K\right)$ which corresponds to moving the basepoints by one full twist around $K$ is trivial. The correction implicitly involves considering the contribution from this (possibly nontrivial) involution in a number of places.