Remark on twists of Frobenius algebra and link homology
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918138011975680 |
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| author | Ito, Noboru Nakagane, Keita Yoshida, Jun |
| author_facet | Ito, Noboru Nakagane, Keita Yoshida, Jun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13731 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Remark on twists of Frobenius algebra and link homology Ito, Noboru Nakagane, Keita Yoshida, Jun Quantum Algebra Geometric Topology 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. |
| title | Remark on twists of Frobenius algebra and link homology |
| topic | Quantum Algebra Geometric Topology |
| url | https://arxiv.org/abs/2508.13731 |