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arXiv · 2305.14212

Symmetric Products and a Cartan-type formula for polyhedral products

A. Bahri·M. Bendersky·F. R. Cohen·S. Gitler
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Abstract

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-Poincar\'e series and to other applications.

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A. Bahri, M. Bendersky, F. R. Cohen, S. Gitler. 2023-05-23. Symmetric Products and a Cartan-type formula for polyhedral products. https://arxiv.org/abs/2305.14212

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