TY - JOUR
T1 - Jacobi identity in polyhedral products
AU - Kishimoto, Daisuke
AU - Matsushita, Takahiro
AU - Yoshise, Ryusei
N1 - Funding Information:
The authors were partially supported by JSPS KAKENHI Grant Numbers JP17K05248 and JP19K03473 (Kishimoto), and JP19K14536 (Matsushita).
Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/5/1
Y1 - 2022/5/1
N2 - 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).
AB - 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).
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U2 - 10.1016/j.topol.2022.108079
DO - 10.1016/j.topol.2022.108079
M3 - Article
AN - SCOPUS:85126691315
SN - 0166-8641
VL - 312
JO - Topology and its Applications
JF - Topology and its Applications
M1 - 108079
ER -