# Link quandles are residually finite

## TL;DR

This paper proves that link quandles are residually finite by extending previous results on free and knot quandles, leveraging the residual finiteness of their associated link groups.

## Contribution

It establishes that free products of residually finite quandles are residually finite if their associated groups are residually finite, confirming residual finiteness for link quandles.

## Key findings

- Link quandles are residually finite.
- Free products of residually finite quandles are residually finite.
- Associated link groups 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 [2] 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.