2025/08/25 by Chauhan, Sachin, Kucharski, Piotr, Noshchenko, Dmitry +3 · 2 citations
#FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2508.18417
We relate the stability of knot invariants under twisting a pair of strands to the stability of symmetric quivers under unlinking (or linking) operation. Starting from the HOMFLY-PT skein relations, we confirm the stable growth of Symr-coloured HOMFLY-PT polynomials under the addition of a~full twist to the knot. On the other hand, we show that symmetric quivers exhibit analogous stable growth under unlinking or linking of the quiver augmented with the extra node; in some cases this augmented quiver captures the spectrum of motivic Donaldson-Thomas invariants of all quivers in the sequence. Combining these two versions of the stable growth, we conjecture that performing a~full twist on any knot corresponds to appropriate unlinking or linking of the corresponding augmented quiver -- this statement is an important step towards a~direct definition of the knot-quiver correspondence based on the knot diagram. We confirm the conjecture for all twist knots, (2,2p+1) torus knots, and all pretzel knots up to 15 crossings with an~odd number of twists in each twist region.