Conjugation quandle detection conjecture for dihedral groups

Let GG be a group, and let the conjugation quandle on GG be the set GG with operation

ab=b1ab.a\triangleright b=b^{-1}ab.

For a link LL, the quandle counting invariant is Hom(Q(L),T)|\operatorname{Hom}(Q(L),T)|, and the Alexander--Conway polynomial is an additional link invariant.

Conjugation quandle detection conjecture. The collection of all conjugation quandles over all dihedral groups is able to detect causality across (2+1)(2+1) globally hyperbolic spacetimes when coupled with the Alexander--Conway polynomial.

The conjecture proposes a universal detection method combining conjugation-quandle data from dihedral groups with the Alexander--Conway polynomial. The source does not establish the claim in full.

Sources & referencesView supporting material

Primary source

Zining Fan, “Detecting Causality with Conjugation Quandles over Dihedral Groups”, arXiv:2509.03544 (2025).

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