Links with finite $n$-quandles

Abstract

We prove a conjecture of Przytycki which asserts that the $n$-quandle of a link $L$ in the 3-sphere is finite if and only if the fundamental group of the $n$-fold cyclic branched cover of the 3-sphere, branched over $L$, is finite.

16 pages, 4 figures, minor revisions in Sections 1-4, new Section 5 added which enumerates all links in $S^3$ with a finite $n$-quandle for some $n$, references added and updated

Cited by in corpus (3)

• N-quandles of links
• Fundamental $n$-quandles of links are residually finite
• Finiteness of canonical quotients of Dehn quandles of surfaces