## Abstract

In this paper we introduce a direct family of simple polytopes Pset;, P^{1},⊂ such that for any 2 ≤ k ≤,n there are non-trivial strictly defined Massey products of order k in the cohomology rings of their moment-angle manifolds ZP^{n}. We prove that the direct sequence of manifolds . set; S3 Z_{Pn} Z_{Pn+1} has the following properties: Every manifold ZPn is a retract of ZPn+1, and one has inverse sequences in cohomology (over n and k, where k → &inf; as n → &inf;) of the Massey products constructed. As an application we get that there are non-trivial differentials dk, for arbitrarily large k as n → &inf; in the Eilenberg.Moore spectral sequence connecting the rings H.(ωX) and H.(X) with coefficients in a field, where X = ZPn.

Original language | English |
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Pages (from-to) | 1081-1136 |

Number of pages | 56 |

Journal | Izvestiya Mathematics |

Volume | 83 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2019 |

Externally published | Yes |

## Keywords

- flag polytope
- generating series
- graph-associahedron
- Lusternik-Schnirelmann category
- Massey product
- moment-angle manifold
- nestohedron
- polyhedral product
- polytope family