Symmetric products and a Cartan-type formula for polyhedral products
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].
scientific article; zbMATH DE number 7921282
scientific article