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This article is cited in 7 scientific papers (total in 7 papers)
On Higher Massey Products and Rational Formality for Moment–Angle Manifolds over Multiwedges
Ivan Yu. Limonchenko National Research University Higher School of Economics, ul. Myasnitskaya 20, Moscow, 101000 Russia
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 $\mathcal Z_K$, and this product contains a unique element (a strictly defined product). Using the simplicial multiwedge construction, we find a family $\mathcal F$ of polyhedral products being smooth closed manifolds such that for any $l,r\geq 2$ there exists an $l$-connected manifold $M\in \mathcal F$ 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 $\Gamma $ to provide a (rationally) formal generalized moment–angle manifold $\mathcal Z_P^J=(\underline {D}^{2j_i},\underline {S}^{2j_i-1})^{\partial P^*}$, $J=(j_1,\dots ,j_m)$, over a graph-associahedron $P=P_{\Gamma }$, and compute all the diffeomorphism types of formal moment–angle manifolds over graph-associahedra.
Keywords:
polyhedral product, moment–angle manifold, simplicial multiwedge, Stanley–Reisner ring, Massey product, graph-associahedron.
Received: October 30, 2018 Revised: December 25, 2018 Accepted: March 14, 2019
Citation:
Ivan Yu. Limonchenko, “On Higher Massey Products and Rational Formality for Moment–Angle Manifolds over Multiwedges”, Algebraic topology, combinatorics, and mathematical physics, Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 75th birthday, Trudy Mat. Inst. Steklova, 305, Steklov Math. Inst. RAS, Moscow, 2019, 174–196; Proc. Steklov Inst. Math., 305 (2019), 161–181
Linking options:
https://www.mathnet.ru/eng/tm4016https://doi.org/10.4213/tm4016 https://www.mathnet.ru/eng/tm/v305/p174
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Abstract page: | 326 | Full-text PDF : | 42 | References: | 33 | First page: | 8 |
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