2025/01/22 by John Chae, Chae, John
Computer Science · #Computational Geometry and Mesh Generation #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2501.12566
openalex publication_date 2025/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide the first computations of colored unknots and Hopf link in ℝℙ3 using both the topological vertex and its refinement. Our approach utilizes the toric Calabi-Yau threefold arising from the geometric transition of the cotangent bundle of ℝℙ3 under the large N duality. We find that the link invariants are series in the Kahler parameters of the toric Calabi-Yau manifold and the q-expansions of the rational functions of the series have positivity property. We conjecture that they are Poincare series of an infinite dimensional link homology theory for links in ℝℙ3. We compare our results with that of the S3 and speculate the consequences of the series nature of the invariants.