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 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 _*(ΩZ _Q), and then studies higher Massey products in H _*(Z _Q) for a graph-associahedron Q.

Keywords

Moment-angle manifold / Flag nestohedra / Stanley-Reisner ring / Massey products / Graph-associahedron

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