Authors: Limonchenko, Ivan 
Title: On Higher Massey Products and Rational Formality for Moment—Angle Manifolds over Multiwedges
Journal: Proceedings of the Steklov Institute of Mathematics
Volume: 305
First page: 161
Last page: 181
Issue Date: 2019
Rank: M22
ISSN: 0081-5438
DOI: 10.1134/S008154381903009X
Abstract: 
We prove that certain conditions on multigraded Betti numbers of a simplicial complex K imply the existence of a higher Massey product in the cohomology of a moment-angle complex ZK, and this product contains a unique element (a strictly defined product). Using the simplicial multiwedge construction, we find a family ℱ of polyhedral products being smooth closed manifolds such that for any l, r ≥ 2 there exists an l-connected manifold M∈ ℱ with a nontrivial strictly defined r-fold Massey product in H*(M). As an application to homological algebra, we determine a wide class of triangulated spheres K such that a nontrivial higher Massey product of any order may exist in the Koszul homology of their Stanley–Reisner rings. As an application to rational homotopy theory, we establish a combinatorial criterion for a simple graph Γ to provide a (rationally) formal generalized moment-angle manifold ZPJ=(D¯2ji,S¯2ji−1)∂P*J = (j1,…,jm), over a graph-associahedron P = PΓ, and compute all the diffeomorphism types of formal moment-angle manifolds over graph-associahedra.
Publisher: Springer Link

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