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 n . 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 -dimensional polytopes P obtained from an n -cube by a sequence of truncations of faces of codimension 2 only (2-truncated cubes). Moreover, the polytopes P are flag nestohedra but not graph-associahedra. The author also describes the numbers β −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 * (Ω Z Q ), and then studies higher Massey products in H * ( Z Q ) for a graph-associahedron Q .