The polyhedral product functor: A method of decomposition for moment-angle complexes, arrangements and related spaces

Bahri, Abbas; Bendersky, Martin; Cohen, Fred; Gitler, S.

doi:10.1016/j.aim.2010.03.026

Cited by 152 publications

(249 citation statements)

References 39 publications

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“…This suggests that the suspension of a polyhedral product ought to be a wedge sum of suspensions of smash polyhedral products where the sum is taken over all full subcomplexes of K. This is exactly what Bahri, Bendersky, Cohen and Gitler proved in [BBCG1].…”

Section: Stable Homotopymentioning

confidence: 74%

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Homotopy theory in toric topology

Grbić¹,

Theriault²

2016

Russ. Math. Surv.

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Abstract. In toric topology, to each simplicial complex K on m vertices one associates two key spaces, the Davis-Januskiewicz space DJ K and the moment-angle complex Z K , which are related by a homotopy fibrationA great deal of work has been done to study properties of DJ K and Z K , their generalisations to polyhedral products, and applications to algebra, combinatorics and geometry.In the first part of this paper we survey some of the main results in the study of the homotopy theory of these spaces. In the second part we break new ground by initiating a study of the map w.We show that, for a certain family of simplicial complexes K, the map w is a sum of higher and iterated Whitehead products.

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Section: Stable Homotopymentioning

confidence: 74%

“…The analogous constructions of DJ K and Z K in (1) and (2) suggest that a generalised functorial construction. This led Buchstaber and Panov [BP2] to define K-powers which later in various work [GT1, DS,BBCG1] developed more fully as polyhedral products. Let K be a simplicial complex on m vertices.…”

Section: Vm] (Z[k] Z)mentioning

confidence: 99%

Homotopy theory in toric topology

Grbić¹,

Theriault²

2016

Russ. Math. Surv.

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“…The maximal faces of L are given by F (µ), as µ varies among the maximal faces of K, with F (µ) = {i ∈ m | µ i = ∞}. The Davis-Januszkiewicz space DJ(K) associated to the multicomplex K is then the generalized moment-angle complex Z(L; X) of [2] for the m-tuple…”

Section: Davis-januszkiewicz Spacesmentioning

confidence: 99%

Generalized Davis-Januszkiewicz spaces, multicomplexes and monomial rings

Trevisan¹

2011

Homology, Homotopy and Applications

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We show that every monomial ring can be realized topologically by a certain topological space. This space is called a generalized Davis-Januszkiewicz space and can be thought of as a colimit over a multicomplex, a combinatorial object generalizing a simplicial complex. Furthermore, we show that such a space is obtained as the homotopy fiber of a certain map with total space the classical Davis-Januszkiewicz space.

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“…A particular case of the following construction, which is the most important one for us here, appeared firstly in the work of Buchstaber and Panov [6] and then was studied intensively and generalized in the works of Bahri, Bendersky, Cohen, Gitler [1], Grbić and Theriault [12], Iriye and Kishimoto [16], and others.…”

Section: Introductionmentioning

confidence: 99%

Topology of moment-angle manifolds arising from flag nestohedra

Limonchenko

2017

Chin. Ann. Math. Ser. B

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Abstract. We construct a family of manifolds, one for each n ≥ 2, having a nontrivial Massey n-product in their cohomology. These manifolds turn out to be smooth closed 2-connected manifolds with a compact torus T m -action called moment-angle manifolds Z P , whose orbit spaces are simple n-dimensional polytopes P obtained from a n-cube by a sequence of truncations of faces of codimension 2 only (2-truncated cubes). Moreover, the polytopes P are flag nestohedra but not graph-associahedra. We compute some bigraded Betti numbers β −i,2(i+1) (Q) for an associahedron Q in terms of its graph structure and relate it to the structure of the loop homology (Pontryagin algebra) H * (ΩZ Q ). We also study triple Massey products in H * (Z Q ) for a graph-associahedron Q.

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The polyhedral product functor: A method of decomposition for moment-angle complexes, arrangements and related spaces

Cited by 152 publications

References 39 publications

Homotopy theory in toric topology

Homotopy theory in toric topology

Generalized Davis-Januszkiewicz spaces, multicomplexes and monomial rings

Topology of moment-angle manifolds arising from flag nestohedra

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