2024/01/19 by Lukas Nakamura, Nakamura, Lukas · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2401.10730
openalex publication_date 2024/01/19 · openalex created_date 2024/01/23 · openalex updated_date 2026/07/28
Inspired by the skein valued open Gromov-Witten theory of Ekholm and Shende and the Gopakumar-Vafa formula, we associate to each pair of non-negative integers (g,l) a formal power series with values in the HOMFLY-PT skein of a disjoint union of l solid tori. The formal power series can be thought of as open BPS-states of genus g with l boundary components and reduces to the contribution of a single BPS state of genus g for l=0. Using skein theoretic methods we show that the formal power series satisfy gluing identities and multi-cover skein relations corresponding to an elliptic boundary node of the underlying curves. For (g,l)=(0,1) we prove a crossing formula which is the multi-cover skein relation corresponding to a hyperbolic boundary node, also known as the pentagon identity.