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Agarwal, S., Grbic, J., Intermont, M. et al. (3 more authors) (Submitted: 2024) Steenrod operations on polyhedral products. [Preprint - arXiv] (Submitted)
Abstract
We describe the action of the mod 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 to polyhedral joins over 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: | Preprint |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 The Author(s). For reuse permissions, please contact the Author(s). |
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 16:28 |
Last Modified: | 29 May 2025 16:28 |
Status: | Submitted |
Identification Number: | 10.48550/arXiv.2401.07919 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:227227 |
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