Massey products, toric topology and combinatorics of polytopes

V. M. Buchstaber, I. Yu Limonchenko

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this paper we introduce a direct family of simple polytopes Pset;, P1,⊂ 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 ZPn. We prove that the direct sequence of manifolds . set; S3 ZPn ZPn+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 languageEnglish
Pages (from-to)1081-1136
Number of pages56
JournalIzvestiya Mathematics
Volume83
Issue number6
DOIs
Publication statusPublished - 2019
Externally publishedYes

Keywords

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

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