Remark on twists of Frobenius algebra and link homology
Fundamenta Mathematicae
MSC: Primary 57K18; Secondary 57K16
DOI: 10.4064/fm250819-12-3
Published online: 27 July 2026
Abstract
We discuss twists on Frobenius algebras in the context of link homology. In his paper in 2006, Khovanov asserted that a twist of a Frobenius algebra yields an isomorphic chain complex on each link diagram. Although the result has been widely accepted for nearly two decades, a subtle gap in the original proof was found in the induction step of the construction of the isomorphism. Following a discussion with Khovanov, we decided to provide a new proof. Our proof is based on a detailed analysis of configurations of circles in each state.
