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
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

Show full item record


checked on May 24, 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.