Whitehead products in moment-angle complexes

Abstract

In toric topology, to a simplicial complex $K$ with $m$ vertices, one associates two spaces, the moment-angle complex ${\mathcal{Z}}_K$ and the Davis-Januszkiewicz space $D{J}_K$. These spaces are connected by a homotopy fibration ${\mathcal{Z}}_K\to D{J}_K\to (\mathbb{C}{P}^{\infty }{)}^m$. In this paper, we show that the map ${\mathcal{Z}}_K\to D{J}_K$ is identified with a wedge of iterated (higher) Whitehead products for a certain class of simplicial complexes $K$ including dual shellable complexes. We will prove the result in a more general setting of polyhedral products.

16 pages, comments welcome