Jacobi identity in polyhedral products

Daisuke Kishimoto, Takahiro Matsushita, Ryusei Yoshise

Research output: Contribution to journalArticlepeer-review


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 for higher Whitehead products (n≥2).

Original languageEnglish
Article number108079
JournalTopology and its Applications
Publication statusPublished - May 1 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


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