English

Quandles versus symmetric quandles for oriented links

Geometric Topology 2020-10-21 v1 Algebraic Topology

Abstract

Given a quandle, we can construct a symmetric quandle called the symmetric double of the quandle. We show that the (co)homology groups of a given quandle are isomorphic to those of its symmetric double. Moreover, quandle coloring numbers and quandle cocycle invariants of oriented links and oriented surface-links can be interpreted by using symmetric quandles.

Keywords

Cite

@article{arxiv.2010.09983,
  title  = {Quandles versus symmetric quandles for oriented links},
  author = {Kanako Oshiro},
  journal= {arXiv preprint arXiv:2010.09983},
  year   = {2020}
}
R2 v1 2026-06-23T19:28:28.585Z