Symmetric products and a Cartan-type formula for polyhedral products
type: Item
instance of: scholarly article
title: Symmetric products and a Cartan-type formula for polyhedral products
DOI: 10.1007/978-3-031-57204-3_3
author: A. Bahri
author: Martin Bendersky
author: F. R. Cohen
author: S. Gitler
publication date: 2024-10-02T00:00:00Z
review text: In this paper the authors give an analogue of the homological Cartan formula for the additive structrue of the homology of the polyhedral product \(Z(K; (X,A))\) of any family of finite, pointed, path-connected \(CW\)-complexes \((X,A)\) over a simplicial complex \(K\). To obtain this the authors extend the ``geometric'' Cartan type formula of the polyhedral smash product \(\widehat{Z}(K; (U,V))\) for wedge decomposable pairs using a novel interplay between polyhedral products and the infinite symmetric products.\N\NAs an application, the Hilber-Poincaré series for the polyhedral product \(Z(K;(X,A)\) is established in terms of the Hilbert-Poincaré series of the links of simplices in full subcomplexes \(K_J\) of \(K\) and associated with spheres and mod-\(p^r\) Moore spaces.\N\NFor the entire collection see [Zbl 1540.57001].
reviewed by: Jelena Grbić
Mathematics Subject Classification ID: 57S12
Mathematics Subject Classification ID: 55Pxx
zbMATH DE Number: 7921282
zbMATH Keywords: polyhedral products
zbMATH Keywords: Cartan formula
zbMATH Keywords: infinite symmetric products
MaRDI profile type: Publication
cites work: Decompositions of the polyhedral product functor with applications to moment-angle complexes and related spaces
cites work: The polyhedral product functor: A method of decomposition for moment-angle complexes, arrangements and related spaces
cites work: A spectral sequence for polyhedral products
cites work: Cellular cochain algebras and torus actions
cites work: Torus actions, combinatorial topology, and homological algebra
cites work: On products in a real moment-angle manifold
cites work: Splitting of certain spaces CX
cites work: Quasifaserungen und unendliche symmetrische Produkte
cites work: The homotopy type of the complement of a coordinate subspace arrangement
cites work: The homotopy type of the polyhedral product for shifted complexes
cites work: Decompositions of polyhedral products for shifted complexes
cites work: Q4730480
cites work: Q4245912
cites work: The cohomology algebra of polyhedral product spaces
cites work: Homotopy types of subspace arrangements via diagrams of spaces
description: scientific article; zbMATH DE number 7921282