Topology of Moment-Angle Manifolds Arising from Flag Nestohedra

The author constructs a family of manifolds, one for each n >= 2, having a nontrivial Massey n-product in their cohomology for any given 71. These manifolds turn out to be smooth closed 2-connected manifolds with a compact torus T-m-action called moment angle manifolds Z(p), whose orbit spaces are simple n-dimensionalpolytopes P obtained from an n-cube by a. sequence of truncations of faces of codimeusiou 2 only (2 truncated cubes). Moreover, the polytopes P are flag nestohedra but not graph-associaltedra. The author also describes the numbers,j beta(-i,) (2(i+1))(Q) for an associahedron Q in terms of its graph structure and relates it to the structure of the loop homology (Pontryagin algebra) H-* (Omega Zeta Q), and then studies higher Massey products in H-*(Zeta Q) for a graph-associahedron Q.