Models for the cohomology of certain polyhedral products
Models for the cohomology of certain polyhedral products
For a commutative ring k with unit, we describe and study various differential graded k-modules and k-algebras as models for the cohomology of polyhedral products (CX, X)K. Along the way, we prove that the integral cohomology H∗((D1, S0)K; Z) of the real moment–angle complex is a Tor module, one that does not come from a geometric setting. As an application, this work sets the stage for studying the based loop space of Σ(CX, X)K.
cohomological models, moment–angle complexes, polyhedral products
37-51
Bendersky, M.
d7098191-6428-4dcb-a9ec-ab83bc44b4de
Grbić, J.
daaea124-d4cc-4818-803a-2b0cb4362175
15 January 2025
Bendersky, M.
d7098191-6428-4dcb-a9ec-ab83bc44b4de
Grbić, J.
daaea124-d4cc-4818-803a-2b0cb4362175
Bendersky, M. and Grbić, J.
(2025)
Models for the cohomology of certain polyhedral products.
Proceedings of the Steklov Institute of Mathematics, 326 (1), , [107837].
(doi:10.1134/S0081543824040047).
Abstract
For a commutative ring k with unit, we describe and study various differential graded k-modules and k-algebras as models for the cohomology of polyhedral products (CX, X)K. Along the way, we prove that the integral cohomology H∗((D1, S0)K; Z) of the real moment–angle complex is a Tor module, one that does not come from a geometric setting. As an application, this work sets the stage for studying the based loop space of Σ(CX, X)K.
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Accepted/In Press date: 12 June 2024
Published date: 15 January 2025
Keywords:
cohomological models, moment–angle complexes, polyhedral products
Identifiers
Local EPrints ID: 498829
URI: http://eprints.soton.ac.uk/id/eprint/498829
ISSN: 0081-5438
PURE UUID: b5c9a9af-c677-4830-a5d1-43f9998f177c
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Date deposited: 03 Mar 2025 17:38
Last modified: 23 Aug 2025 01:58
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Author:
M. Bendersky
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