arXiv subjects

Jonathan A. Higgins

Publications and source records attributed to Jonathan A. Higgins.

2 recordsLinked to original sources

arXiv2026

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

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.

math.GT↗

arXiv2026

A Geometric Approach to the Links-Quivers Correspondence II: Rational Links

The Links-Quivers Correspondence predicts that the generating function for the symmetric (or antisymmetric) colored HOMFLY-PT polynomials for links can be put in a "quiver form," so that the generating function is expressed in terms of a quadratic form and two linear forms. This was originally proved for rational links by Stosic and Wedrich, but here we give a direct geometric description of the linear and quadratic forms in terms of the first and second configuration spaces of the 3-punctured plane.

math.GT↗