2023/05/23 by Bahri, A., Bendersky, M., Cohen, F. R. +1
#13F55 Secondary:14F45 #55N10 #55T10 #55U10 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Primary: 55B11
paper · doi:10.48550/arxiv.2305.14212
We give a geometric method for determining the cohomology groups of a polyhedral product under suitable freeness conditions or with coefficients taken in a field. This is done by considering first the special case for which the pairs of spaces are wedge decomposable. We derive a decomposition for these polyhedral products which resembles a Cartan formula. The theory of symmetric products is used then to generalize the result to polyhedral products involving arbitrary pairs. This leads to a direct computation of the Hilbert-Poincaré series and to other applications.