Correction to the article Floer homology and splicing knot complements

Eftekhary, Eaman

doi:10.2140/agt.2020.20.3205

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Correction to the article Floer homology and splicing knot complements

Eaman Eftekhary

Algebraic & Geometric Topology 20 (2020) 3205–3218

DOI: 10.2140/agt.2020.20.3205

Correction to Algebraic & Geometric Topology 15:6 (2015) 3155–3213

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 $\hat{HFK} (K)$ 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.

Keywords

Floer homology, splicing, essential torus

Mathematical Subject Classification 2010

Primary: 57M27

Secondary: 57R58

References

Publication

Received: 28 October 2017

Revised: 21 January 2020

Accepted: 5 February 2020

Published: 8 December 2020

Authors

Eaman Eftekhary
School of Mathematics Institute for Research in Fundamental Sciences (IPM) Tehran Iran
http://math.ipm.ir/~eftekhary

Volume 20, issue 6 (2020)