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arXiv · 2508.13731

Remark on twists of Frobenius algebra and link homology

Noboru Ito·Keita Nakagane·Jun Yoshida
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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 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.

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Noboru Ito, Keita Nakagane, Jun Yoshida. 2025-08-19. Remark on twists of Frobenius algebra and link homology. https://arxiv.org/abs/2508.13731

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