English

A Geometric Approach to the Links-Quivers Correspondence I: Rational Tangles

Geometric Topology 2026-03-03 v1 Quantum Algebra

Abstract

The Links-Quivers Correspondence predicts that all the symmetric (or antisymmetric) colored HOMFLY-PT polynomials of a link can be recovered from a finite amount of data (a quiver) associated to the link. We give a new geometric proof of the Links-Quivers Correspondence modified for rational tangles and explicitly describe the corresponding quivers in terms of winding numbers in the punctured plane and its second configuration space.

Keywords

Cite

@article{arxiv.2603.01303,
  title  = {A Geometric Approach to the Links-Quivers Correspondence I: Rational Tangles},
  author = {Jonathan A. Higgins},
  journal= {arXiv preprint arXiv:2603.01303},
  year   = {2026}
}

Comments

58 pages, many figures