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
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.

Show full item record


checked on May 23, 2024

Page view(s)

checked on May 9, 2024

Google ScholarTM




Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.