Twisted Yang-Baxter sets, cohomology theory, and application to knots

Mohamed Elhamdadi; Manpreet Singh

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arXiv · 2401.01533

Twisted Yang-Baxter sets, cohomology theory, and application to knots

Mohamed Elhamdadi·Manpreet Singh

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Abstract

We introduce twisted set-theoretic Yang-Baxter solutions and develop an associated cohomology theory, which extends the standard cohomology theory of Yang-Baxter solutions. By employing cocycles of twisted biquandles along with Alexander numbering, we construct state-sum invariants for knots and knotted surfaces. As an application, we use our approach to distinguish the $2$-twist spun trefoil from its reverse orientation, in line with prior findings.

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Mohamed Elhamdadi, Manpreet Singh. 2024-01-03. Twisted Yang-Baxter sets, cohomology theory, and application to knots. https://arxiv.org/abs/2401.01533

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