Non-isomorphism conjecture for quandles constructed from an infinite-type quandle

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Let QQ be an infinite type quandle. For each positive integer nn, let d4acn(Q)d4ac_n(Q) denote the quandle constructed from QQ at level nn.

Non-isomorphism conjecture. The quandles d4acn(Q)d4ac_n(Q) and d4acm(Q)d4ac_m(Q) are not isomorphic whenever n≠mn\neq m and n,m∈Z+n,m\in\mathbb{Z}^+.

This conjecture asserts that the construction produces pairwise non-isomorphic quandles from an infinite-type quandle. The supplied text gives no information about whether it has been resolved.

References

Primary source

Pedro Lopes and Manpreet Singh, “Constructing an infinite family of quandles from a quandle”, arXiv:2211.13360 (2022).

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