Secant-quandle: an invariant of braids and knots

Yangzhou Liu; Seongjeong Kim; Vassily Olegovich Manturov

Secant-quandle: an invariant of braids and knots

Geometric Topology 2026-03-27 v1 Algebraic Topology

Authors: Yangzhou Liu , Seongjeong Kim , Vassily Olegovich Manturov

Abstract

We construct a novel invariant of braids and knots, secant-quandle (SQ),with generic secants serving as generators and generic horizontal trisecants serving as relations, i.e., $SQ = \Gamma \left< \mathcal{S}_M\mid \mathcal{S}_T,\mathcal{E}_M \right>$ , where $M$ is a braid or link.

Keywords

secant-quandle braid knot invariant quandle

Cite

@article{arxiv.2603.25256,
  title  = {Secant-quandle: an invariant of braids and knots},
  author = {Yangzhou Liu and Seongjeong Kim and Vassily Olegovich Manturov},
  journal= {arXiv preprint arXiv:2603.25256},
  year   = {2026}
}

Comments

16 pages, 9 figures, Presented at H. Kauffman's Quantum Topology Conference

Secant-quandle: an invariant of braids and knots

Abstract

Keywords

Cite

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