Nontorus link from topological vertex

2018/06/30 by H. Awata, Hidetoshi Awata, H. Kanno +7
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Braid #Combinatorics #Conifold #Formalism (music) #Geometric and Algebraic Topology #Graph #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Knot theory #Link (geometry) #Mathematics #Pure mathematics #Tangle #Topology (electrical circuits) #Vertex (graph theory) #hep-th #math.GT #math.QA

paper · pdf · doi:10.1103/physrevd.98.046018

published as Phys. Rev. D 98, 046018 (2018) · 18 pages

arxiv created 2018/08/22 · openalex publication_date 2018/08/27 · arxiv updated 2018/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The recently suggested tangle calculus for knot polynomials is intimately related to topological string considerations and can help to build the HOMFLY-PT invariants from the topological vertices. We discuss this interplay in the simplest example of the Hopf link and link L_8n8. It turns out that the resolved conifold with four different representations on the four external legs, on the topological string side, is described by a special projection of the four-component link L_8n8, which reduces to the Hopf link colored with two composite representations. Thus, this provides the first explicit example of non-torus link description through topological vertex. It is not a real breakthrough, because L_8n8 is just a cable of the Hopf link, still it can help to intensify the development of the formalism towards more interesting examples.

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