Topology of moment-angle manifolds arising from flag nestohedra

Abstract

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 Tm-action called moment-angle manifolds ZP, 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*(ΩZQ), and then studies higher Massey products in H*(ZQ) for a graph-associahedron Q.