Discrete Morse theory for moment-angle complexes of pairs (D^n,S^{n-1})

Abstract: For a finite simplicial complex K and a CW-pair (X,A), there is an associated CW-complex Z_K(X,A), known as a polyhedral product. 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 vertex-decomposable dual is homotopy equivalent to a wedge of spheres.