Moment-angle complexes of pairs (Dn,Sn-1) and Simplicial complexes with vertex-decomposable duals

We study for a finite simplicial complex K and a CW-pair ( X , A ) the associated CW-complex Z K ( X , A ) , known as the polyhedral product or generalized moment angle-complex. We apply discrete Morse theory to a particular CW-structure on the n -sphere moment-angle complexes Z K ( D n , S n - 1 ) . For the class of simplicial complexes with vertex-decomposable duals, we show that the associated n -sphere moment-angle complexes have the homotopy type of wedges of spheres. As a corollary we show that a sufficiently high suspension of any restriction of a simplicial complex with the vertex-decomposable dual is homotopy equivalent to a wedge of spheres.