Massey products in cohomology of moment-angle manifolds corresponding to Pogorelov polytopes

Zhuravleva, Elizaveta Grigor'evna

doi:10.48550/arxiv.1707.07365

Cited by 3 publications

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“…Using Theorem 6.6 (2) and Theorem 6.1 (1), Grbić and Linton obtain a result due to Zhuravleva [75], who proved that for any Pogorelov polytope P (see [71,1,21,22]) there exists a non-trivial triple Massey product in H * (Z P ).…”

Section: Massey Products In Toric Topology and Nonformality Of Polyhe...mentioning

confidence: 99%

Higher order Massey products and applications

Limonchenko¹,

Миллионщиков²

2020

Preprint

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Section: Massey Products In Toric Topology and Nonformality Of Polyhe...mentioning

confidence: 99%

Higher order Massey products and applications

Limonchenko¹,

Миллионщиков²

2020

Preprint

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“…Then the moment-angle complex Z P = Z K P is a (polytopal) moment-angle manifold. Zhuravleva [13] showed that for any Pogorelov polytope P , moment-angle manifolds Z P have a non-trivial triple Massey product using the full subcomplex in Figure 10. .…”

Section: Theorem 321 ([1]mentioning

confidence: 99%

“…. A full subcomplex of the simplicial complex corresponding to any Pogorelov polytope [13] Applying edge contractions to the coloured edges of the full subcomplex in Figure 10, we obtain the simplicial complex in Figure 11. This simplicial complex has a non-trivial triple Massey product, as can be shown by direct calculation (an identical calculation to Example 2.5).…”

Section: Theorem 321 ([1]mentioning

confidence: 99%

“…The first examples of non-trivial higher Massey products in moment-angle complexes were found in 2003 by Baskakov [3], who gave an infinite family of momentangle complexes with non-trivial triple Massey products. Since then, there have been other families of examples such as Limonchenko's family of n-Massey products in moment-angle complexes over truncated cubes [10], and Zhuravleva found non-trivial triple Massey products over Pogorelov polytopes [13]. There is also a classification of non-trivial triple Massey products in the lowest degree [7,8].…”

Section: Introductionmentioning

confidence: 99%

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Non-trivial higher Massey products in moment-angle complexes

Grbić¹,

Linton²

2019

Preprint

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We describe two different systematic constructions of new nontrivial higher Massey products in the cohomology of moment-angle complexes, using homotopy theory and combinatorial operations. These constructions in conjunction detect non-trivial higher Massey products in the cohomology of moment-angle manifolds corresponding to polytopes such as families of graph associahedra. Our constructions use stellar subdivisions and edge contractions on simplicial complexes. These operations do not change the homotopy type of a simplicial complex, but do change the combinatorics, which changes the corresponding moment-angle complex.

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“…Using this result, we prove a necessary and sufficient condition in terms of combinatorics of a simple graph Γ to provide a moment-angle manifold Z P over a graph-associahedron P = P Γ with a nontrivial triple Massey product in H * (Z P ), see Lemma 4.9. Recently, it was shown in [51] that there exists a nontrivial triple Massey product in H * (Z P ) for any Pogorelov polytope P (the latter class of 3dimensional flag simple polytopes contains, in particular, all fullerenes). First examples of polyhedral products with nontrivial n-fold Massey products in cohomology for any n ≥ 2 were constructed in [38,39].…”

Section: Introductionmentioning

confidence: 99%

Topology of polyhedral products over simplicial multiwedges

Limonchenko¹

2017

Preprint

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We prove that certain conditions on multigraded Betti numbers of a simplicial complex K imply existence of a higher Massey product in cohomology of a moment-angle-complex Z K , which 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 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 Z J P = (D ¯2ji , S ¯2ji−1 ) ∂P * , J = (j 1 , . . . , j m ) over a graphassociahedron P = P Γ and compute all the diffeomorphism types of formal moment-angle manifolds over graph-associahedra.

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Massey products in cohomology of moment-angle manifolds corresponding to Pogorelov polytopes

Cited by 3 publications

References 0 publications

Higher order Massey products and applications

Higher order Massey products and applications

Non-trivial higher Massey products in moment-angle complexes

Topology of polyhedral products over simplicial multiwedges

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