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

Abstract

We study for a finite simplicial complex K and a CW-pair (X,A) the associated CW-complex (Formula presented.), 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 (Formula presented.). 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.