Polyhedral products for shifted complexes and higher Whitehead products

Abstract

This paper studies the map between polyhedral products ${\mathcal{Z}}_K(C\underline{X},\underline{X})\to {\mathcal{Z}}_K(\Sigma \underline{X},\ast )$ induced from the pinch maps $(C{X}_i,X_i)\to (\Sigma X_i,\ast )$, which is the higher order Whitehead product if $K$ is the boundary of a simplex. When $K$ is a shifted complex, a wedge decomposition of ${\mathcal{Z}}_K(C\underline{X},\underline{X})$ is given by the authors. Based on this decomposition, when $K$ is shifted, the induced pinch map is explicitly described as a wedge of iterated Whitehead products each of which includes at most one higher product. As a corollary, the Jacobi identity of Whitehead products including higher products due to Hardie is generalized.

The new paper "Whitehead products in moment-angle complexes" by the authors includes more general results

References in corpus (1)

• Decompositions of suspensions of spaces involving polyhedral products

Cited by in corpus (3)

• Higher order Whitehead products and $L_{\infty }$ structures on the homology of a DGL
• Higher Whitehead products in moment-angle complexes and substitution of simplicial complexes
• On the higher order exterior and interior Whitehead products