Work

Quandle action quivers

Year: 2025

Type: article

Abstract: Quandle Coloring Quivers are directed graph-valued invariants of classical and virtual knots and links associated to finite quandles. Quandle action quivers are subquivers of the full quandle coloring quiver associated to quandle actions by elements of the coloring quandle. These quivers provide a categorification of the quandle counting invariant associated to each element of the quandle. We obtain new polynomial invariants called quandle action polynomials from these quivers as decategorifications.

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s0218216525500300

Authors: Mason Cai, Sam Nelson

Institutions: Pomona College, Claremont McKenna College

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Simons Foundation

Award: G6817113029