Authors: Buchstaber, V. M.
Limonchenko, Ivan 
Title: Massey products, toric topology and combinatorics of polytopes
Journal: Izvestiya: Mathematics
Volume: 83
Issue: 6
First page: 1081
Last page: 1136
Issue Date: 2019
Rank: M21
ISSN: 1064-5632
DOI: 10.1070/im8927
Abstract: 
In this paper we introduce a direct family of simple polytopes P0⊂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 ∗⊂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→∞ as n→∞) of the Massey products constructed. As an application we get that there are non-trivial differentials dk, for arbitrarily large k as n→∞, in the Eilenberg–Moore spectral sequence connecting the rings H∗(ΩX) and H∗(X) with coefficients in a field, where X=ZPn.
Keywords: polyhedral product | moment-angle manifold | Massey product | Lusternik–Schnirelmann category | polytope family | flag polytope | generating series | nestohedron | graph-associahedron
Publisher: Russian Academy of Sciences; London Mathematical Society in partnership with Turpion Ltd.

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