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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