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math.GT2024
Connections between conjugation quandles and their underlying groups via residual finiteness and the Hopf property
Mohamed Elhamdadi, Jan Kim
We prove that if a conjugation quandle is Hopfian, then its underlying group is also Hopfian. We also show that the converse does not hold by providing an example. This highlights…
math.GT2024
Twisted Yang-Baxter sets, cohomology theory, and application to knots
Mohamed Elhamdadi, Manpreet Singh
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 empl…