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 Rr for any r≥1, has the homotopy type of a wedge of spheres.