Decompositions of polyhedral products for shifted complexes

The conjecture of Bahri, Bendersky, Cohen and Gitler (2010)  3] on wedge decompositions of polyhedral products of shifted complexes is settled affirmatively. As a corollary, it is proved that the homotopy type of the complement of a coordinate subspace arrangement associated with a shifted complex, tensored with R^r${\mathbb{R}}^r$ for any r≥1$r\ge 1$, has the homotopy type of a wedge of spheres.