English

Links with finite $n$-quandles

Geometric Topology 2018-03-16 v2

Abstract

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

Cite

@article{arxiv.1606.08324,
  title  = {Links with finite $n$-quandles},
  author = {Jim Hoste and Patrick D. Shanahan},
  journal= {arXiv preprint arXiv:1606.08324},
  year   = {2018}
}

Comments

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

R2 v1 2026-06-22T14:35:19.601Z