Decompositions of the polyhedral product functor with applications to moment-angle complexes and related spaces

DOI10.1073/pnas.0905159106zbMath1203.57009OpenAlexW2022786738WikidataQ37268810 ScholiaQ37268810MaRDI QIDQ3069220

Martin Bendersky, Anthony Bahri, Frederick R. Cohen, Samuel Gitler

Publication date: 24 January 2011

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1073/pnas.0905159106

zbMATH Keywords

arrangementstoric varietiesStanley-Reisner ring

Mathematics Subject Classification ID

Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Abstract and axiomatic homotopy theory in algebraic topology (55U35) Polyhedral manifolds (52B70) PL-topology (57Q99)

Related Items

Vector bundles over Davis-Januszkiewicz spaces with prescribed characteristic classes, Orbit configuration spaces of small covers and quasi-toric manifolds, The cohomology algebra of polyhedral product spaces, The polyhedral product functor: A method of decomposition for moment-angle complexes, arrangements and related spaces, On problems concerning moment-angle complexes and polyhedral products, The \(KO^\ast\)-rings of \(BT^m\), the Davis-Januszkiewicz spaces and certain toric manifolds, Right-angularity, flag complexes, asphericity, Cohomology computations for Artin groups, Bestvina-Brady groups, and graph products., Möbius transform, moment-angle complexes and Halperin-Carlsson conjecture, A spectral sequence for polyhedral products, The complement of polyhedral product spaces and the dual simplicial complexes, Cup-products for the polyhedral product functor, On the (co)homology of (quotients of) moment-angle manifolds over polygons

Cites Work

• Convex polytopes, Coxeter orbifolds and torus actions
• Algebraic invariants for right-angled Artin groups.
• The configuration space of the \(n\)-arms machine in the Euclidean space
• Moment-angle complexes, monomial ideals and Massey products
• Homotopy types of subspace arrangements via diagrams of spaces
• Complements of sphere and subspace arrangements
• On the complements of affine subspace arrangements
• On Davis-Januszkiewicz homotopy types I: formality and rationalisation
• Wonderful models of subspace arrangements
• The integral cohomology of toric manifolds
• Reduced product spaces
• Torus actions, combinatorial topology, and homological algebra
• Cohomology ofK-powers of spaces and the combinatorics of simplicial divisions
• Cellular cochain algebras and torus actions
• Massey triple products in the cohomology of moment-angle complexes
• Homotopy type of the complement of a coordinate subspace arrangement of codimension two
• The Homotopy Groups of Wedges of Suspensions
• The cohomology rings of complements of subspace arrangements
• The cohomology algebra of the complement of a finite family of affine subspaces in an affine space. (L'algèbre de cohomologie du complément, dans un espace affine, d'une famille finie de sous-espaces affines).