Link quandles are residually finite

Abstract

Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work (Bardakov et al. in Proc Am Math Soc 147:3621–3633, 2019. https://doi.org/10.1090/proc/14488) residual finiteness of quandles was introduced, and it was proved that free quandles and knot quandles are residually finite. In this paper, we extend these results and prove that free products of residually finite quandles are residually finite provided their associated groups are residually finite. As associated groups of link quandles are link groups, which are known to be residually finite, it follows that link quandles are residually finite.