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arXiv · 2111.12199

Jacobi identity in polyhedral products

Daisuke Kishimoto·Takahiro Matsushita·Ryusei Yoshise
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Abstract

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 ($n\ge 2$).

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Daisuke Kishimoto, Takahiro Matsushita, Ryusei Yoshise. 2021-11-23. Jacobi identity in polyhedral products. https://arxiv.org/abs/2111.12199

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