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

Jonathan A. Higgins

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arXiv · 2603.01303

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

Jonathan A. Higgins

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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.

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Jonathan A. Higgins. 2026-03-01. A Geometric Approach to the Links-Quivers Correspondence I: Rational Tangles. https://arxiv.org/abs/2603.01303

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