Tangle addition and the knots-quivers correspondence
arXiv:2004.10837 · doi:10.1112/jlms.12433
Abstract
We prove that the generating functions for the one row/column colored HOMFLY-PT invariants of arborescent links are specializations of the generating functions of the motivic Donaldson-Thomas invariants of appropriate quivers that we naturally associate with these links. Our approach extends the previously established tangles-quivers correspondence for rational tangles to algebraic tangles by developing gluing formulas for HOMFLY-PT skein generating functions under Conway's tangle addition. As a consequence, we prove the conjectural links-quivers correspondence of Kucharski-Reineke-Stošić-Sulkowski for all arborescent links.
arXiv comment24 pages, page numbers differ from published version
References in corpus (18)
- Knot Invariants and Topological Strings
- Matrix factorizations and link homology II
- Knots, links and branes at large N
- The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
- Webs and quantum skew Howe duality
- Cohomological Hall algebra of a symmetric quiver
- Knots-quivers correspondence
- The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link
- BPS states, knots and quivers
- Super -Howe duality and web categories
- Tabulating knot polynomials for arborescent knots
- Topological strings, strips and quivers
- Donaldson-Thomas invariants, torus knots, and lattice paths
- The colored HOMFLYPT function is -holonomic
- Rational links and DT invariants of quivers
- Categorified sl(N) invariants of colored rational tangles
- q-holonomic formulas for colored HOMFLY polynomials of 2-bridge links
- Khovanov invariants via Fukaya categories: the tangle invariants agree