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 com...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 momentangle 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_*(?ZQ), and then studies higher Massey products in H*(ZQ) for a graph-associahedron Q.展开更多
基金supported by the General Financial Grant from the China Postdoctoral Science Foundation(No.2016M601486)
文摘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 momentangle 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_*(?ZQ), and then studies higher Massey products in H*(ZQ) for a graph-associahedron Q.
