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Agarwal, S., Grbić, J., Intermont, M. et al. (3 more authors) (2025) Steenrod operations on polyhedral products. Topology and its Applications. 109446. ISSN 0166-8641
Abstract
We describe the action of the mod 2 Steenrod algebra on the cohomology of various polyhedral products and related spaces. We carry this out for Davis-Januszkiewicz spaces and their generalizations, for moment-angle complexes as well as for certain polyhedral joins. By studying the combinatorics of underlying simplicial complexes, we deduce some consequences for the lowest cohomological dimension in which non-trivial Steenrod operations can appear.
We present a version of cochain-level formulas for Steenrod operations on simplicial complexes. We explain the idea of “propagating” such formulas from a simplicial complex K to polyhedral joins over K and we give examples of this process. We tie the propagation of the Steenrod algebra actions on polyhedral joins to those on moment-angle complexes. Although these are cases where one can understand the Steenrod action via a stable homotopy decomposition, we anticipate applying this method to cases where there is no such decomposition.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2025 The Authors. Except as otherwise noted, this author-accepted version of a journal article published in Topology and its Applications is made available via the University of Sheffield Research Publications and Copyright Policy under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematical and Physical Sciences |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 29 May 2025 16:24 |
Last Modified: | 30 May 2025 13:32 |
Status: | Published online |
Publisher: | Elsevier BV |
Refereed: | Yes |
Identification Number: | 10.1016/j.topol.2025.109446 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:227240 |
Available Versions of this Item
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Steenrod operations on polyhedral products. (deposited 29 May 2025 16:28)
- Steenrod operations on polyhedral products. (deposited 29 May 2025 16:24) [Currently Displayed]