Finite residuality of involutory quandles of knots
Let be a knot diagram, and let denote its involutory quandle. An involutory quandle is trivial if it consists of one element.
Involutory quandles are finitely residual. If is non-trivial, then there is a finite non-trivial involutory quandle and a surjective homomorphism
This is presented as equivalent to the finite countermodel property needed for the proposed unknot-detection programme to become a decision procedure; the source gives no resolution of the conjecture.
References
Primary source
Andrew Fish and Alexei Lisitsa, “Detecting unknots via equational reasoning, I: Exploration”, arXiv:1405.4211 (2014).
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