Decompositions of polyhedral products for shifted complexes

DOI10.1016/j.aim.2013.05.003zbMath1419.55010arXiv1505.04892OpenAlexW2031449044MaRDI QIDQ2437492

Kouyemon Iriye, Daisuke Kishimoto

Publication date: 3 March 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.04892

zbMATH Keywords

polyhedral productsubspace arrangementhomotopy decompositionshifted complex

Mathematics Subject Classification ID

Classification of homotopy type (55P15) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35)

Related Items (22)

Whitehead products in moment-angle complexes ⋮ The dual polyhedral product, cocategory and nilpotence ⋮ Jacobi identity in polyhedral products ⋮ On the moment-angle manifold constructed by Fan, Chen, Ma and Wang ⋮ \(A_\infty\)-resolutions and the Golod property for monomial rings ⋮ Pure vertex decomposable simplicial complex associated to graphs whose 5-cycles are chorded ⋮ Higher order Massey products and applications ⋮ Topology of moment-angle manifolds arising from flag nestohedra ⋮ Golod and tight 3-manifolds ⋮ Characterisation of polyhedral products with finite generalised Postnikov decomposition ⋮ On the higher Whitehead product ⋮ On the higher order exterior and interior Whitehead products ⋮ Higher order Whitehead products and \(L_{\infty}\) structures on the homology of a DGL ⋮ A Golod complex with non-suspension moment-angle complex ⋮ Moment-angle complexes of pairs \((D^n,S^{n-1})\) and simplicial complexes with vertex-decomposable duals ⋮ Higher Whitehead products in moment-angle complexes and substitution of simplicial complexes ⋮ On higher Massey products and rational formality for moment-angle manifolds over multiwedges ⋮ Massey products, toric topology and combinatorics of polytopes ⋮ Moore's conjecture for polyhedral products ⋮ Fat-wedge filtration and decomposition of polyhedral products ⋮ Iterated higher Whitehead products in topology of moment-angle complexes ⋮ Configuration spaces and polyhedral products

Cites Work

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• Cohomology computations for Artin groups, Bestvina-Brady groups, and graph products.
• Convex polytopes, Coxeter orbifolds and torus actions
• The homotopy type of the complement of a coordinate subspace arrangement
• Moment-angle complexes, monomial ideals and Massey products
• Higher order Whitehead products
• The polyhedral product functor: A method of decomposition for moment-angle complexes, arrangements and related spaces
• Rational homotopy of the polyhedral product functor
• Pull-Backs in Homotopy Theory
• Cohomology ofK-powers of spaces and the combinatorics of simplicial divisions
• Colorings of simplicial complexes and vector bundles over Davis-Januszkiewicz spaces

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