Work

Generalized knots–quivers correspondence

Year: 2025

Type: article

Abstract: We propose a generalized version of knots–quivers correspondence, where the quiver series variables specialize to arbitrary powers of the knot HOMFLY-PT polynomial series variable. We explicitly compute quivers for large classes of knots, as well as many homologically thick 9- and 10-crossings knots, including the ones with the super-exponential growth property of colored HOMFLY-PT polynomials. In addition, we propose a new, compact, quiver-like form for the colored HOMFLY-PT polynomials, where the structure of colored differentials is manifest. In particular, this form partially explains the non-uniqueness of quivers corresponding to a given knot via knots–quivers correspondence.

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s0218216525500531

Author: Marko Stošić

Institutions: Serbian Academy of Sciences and Arts, University of Lisbon, Mathematical Institute of the Serbian Academy of Sciences and Arts

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Science Fund of the Republic of Serbia, Fundação para a Ciência e a Tecnologia

Awards: Centro de Estudos Matemáticos de Ciências, ULisboa, G4118941449, G8718594641