2026/07/27 by Noboru Ito, Keita Nakagane, Jun Yoshida
paper · doi:10.4064/fm250819-12-3
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.