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.
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