2021/11/23 by Daisuke Kishimoto, Kishimoto, Daisuke, Takahiro Matsushita +3
Mathematics · #55P15 #55Q15 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2111.12199
openalex publication_date 2021/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that a relation among minimal non-faces of a fillable complex K yields an identity of iterated (higher) Whitehead products in a polyhedral product over K. In particular, for the (n-1)-skeleton of a simplicial n-sphere, we always have such an identity, and for the (n-1)-skeleton of a (n+1)-simplex, the identity is the Jacobi identity of Whitehead products (n=1) and Hardie's identity of higher Whitehead products (n≥ 2).