Steenrod operations on polyhedral products
Steenrod operations on polyhedral products
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.
Moment-angle complex, Polyhedral joins, Polyhedral product, Steenrod operation
Agarwal, Sanjana
08166d48-f90d-497c-bee9-06a309ad0abc
Grbić, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Intermont, Michele
d9cdb0ed-612e-4f78-bff1-9601c9618650
Jovanović, Milica
30ed1801-ebba-4165-b18a-c66805b6ff43
Lagoda, Evgeniya
7d04f9fd-48cb-4ebc-8db4-356243f21c96
Whitehouse, Sarah
392be7ec-37e1-4f59-bd6b-e34ac0033ccf
Agarwal, Sanjana
08166d48-f90d-497c-bee9-06a309ad0abc
Grbić, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Intermont, Michele
d9cdb0ed-612e-4f78-bff1-9601c9618650
Jovanović, Milica
30ed1801-ebba-4165-b18a-c66805b6ff43
Lagoda, Evgeniya
7d04f9fd-48cb-4ebc-8db4-356243f21c96
Whitehouse, Sarah
392be7ec-37e1-4f59-bd6b-e34ac0033ccf
Agarwal, Sanjana, Grbić, Jelena, Intermont, Michele, Jovanović, Milica, Lagoda, Evgeniya and Whitehouse, Sarah
(2025)
Steenrod operations on polyhedral products.
Topology and its Applications, [109446].
(doi:10.1016/j.topol.2025.109446).
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.
Text
Steenrod operations on polyhedral products
- Accepted Manuscript
Restricted to Repository staff only until 27 May 2027.
Request a copy
More information
Accepted/In Press date: 10 June 2024
e-pub ahead of print date: 27 May 2025
Keywords:
Moment-angle complex, Polyhedral joins, Polyhedral product, Steenrod operation
Identifiers
Local EPrints ID: 503588
URI: http://eprints.soton.ac.uk/id/eprint/503588
ISSN: 0166-8641
PURE UUID: ea003f27-b387-4ac4-9e25-0fd3560ca85b
Catalogue record
Date deposited: 05 Aug 2025 16:58
Last modified: 06 Aug 2025 01:46
Export record
Altmetrics
Contributors
Author:
Sanjana Agarwal
Author:
Michele Intermont
Author:
Milica Jovanović
Author:
Evgeniya Lagoda
Author:
Sarah Whitehouse
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
