2024/07/01 by Polina Evgen'evna Zakorko, Zakorko, Polina, Polina Aleksandrovna Zinova +1
Mathematics · #57K14 #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2407.01144
openalex publication_date 2024/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The \mathfraksl2 weight system, corresponding to the colored Jones polynomial of knots, is one of the the simplest weight system for chord diagrams. Recent works have led to explicit computations of this weight system on chord diagrams with complete and complete bipartite intersection graphs using \mathfraksl2 weight systems on shares, i.e., on chord diagrams on two strands. In this paper, we continue our study of shares. We prove a conjecture by Lando about a duality of values of the \mathfraksl2 weight system on chord diagrams whose intersection graphs are joins of complementary graphs with discrete ones. To achieve this, we introduce the two-colored intersection graph of shares, define the inner product of shares, and use chord-adding operators.