2020/09/15 by Abbas Bahri, Bahri, A., Martin Bendersky +5
Mathematics · #13F55 #14M25 #55N10 #55T10 #55U10 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Primary: 52B11 #Secondary: 14F45 #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2009.06818
openalex publication_date 2020/09/15 · openalex created_date 2020/09/21 · openalex updated_date 2026/07/28
We give a geometric method for determining the cohomology groups and the product structure of a polyhedral product, under suitable freeness conditions or with coefficients taken in a field. This is done by considering first a special class of CW pairs for which we derive a decomposition of the polyhedral product resembling a Cartan formula. The result is then generalized to arbitrary CW pairs of finite type. This leads to a direct computation of the Hilbert-Poincaré series and to other applications. The product structure on the cohomology of the polyhedral product is computed in terms of the additive generators, labelled via the Cartan decomposition. The description given suffices to enable explicit calculations.