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Realizing orders in rational sphere product algebras with three generators

Realizing orders in rational sphere product algebras with three generators
Realizing orders in rational sphere product algebras with three generators
The realization problem asks which algebras can be realized as the cohomology of spaces. We study this problem in the context of the orders in a graded rational exterior algebra on three generators. An order is a subring whose underlying additive group is a lattice. We give conditions for when such an order is realizable, and in particular show that in the simply-connected case any order is realizable if the generators of the exterior algebra are of odd degree.
cohomology realization problem, graded order, polyhedral product, Graded order, Cohomology realization problem, Polyhedral product
0022-4049
So, Tseleung
d0bdbf03-7034-4f97-a34d-2c0499cb97ed
Stanley, Donald
3124e678-eef2-4f3b-9bd1-d4f00c0cfd1b
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Williams, Ben
9fabea3e-f7b8-485d-b4f5-188140d67c83
So, Tseleung
d0bdbf03-7034-4f97-a34d-2c0499cb97ed
Stanley, Donald
3124e678-eef2-4f3b-9bd1-d4f00c0cfd1b
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Williams, Ben
9fabea3e-f7b8-485d-b4f5-188140d67c83

So, Tseleung, Stanley, Donald, Theriault, Stephen and Williams, Ben (2026) Realizing orders in rational sphere product algebras with three generators. Journal of Pure and Applied Algebra, 230 (10), [108333]. (doi:10.1016/j.jpaa.2026.108333).

Record type: Article

Abstract

The realization problem asks which algebras can be realized as the cohomology of spaces. We study this problem in the context of the orders in a graded rational exterior algebra on three generators. An order is a subring whose underlying additive group is a lattice. We give conditions for when such an order is realizable, and in particular show that in the simply-connected case any order is realizable if the generators of the exterior algebra are of odd degree.

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ThreePoint revised - Accepted Manuscript
Restricted to Repository staff only until 2 July 2027.
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Accepted/In Press date: 8 June 2026
e-pub ahead of print date: 2 July 2026
Published date: 15 July 2026
Keywords: cohomology realization problem, graded order, polyhedral product, Graded order, Cohomology realization problem, Polyhedral product

Identifiers

Local EPrints ID: 513694
URI: https://eprints.soton.ac.uk/id/eprint/513694
DOI: doi:10.1016/j.jpaa.2026.108333
ISSN: 0022-4049
PURE UUID: d00fe8d9-1b4c-43dc-b9c4-d67798c73b24
ORCID for Stephen Theriault: ORCID iD orcid.org/0000-0002-7729-5527

Catalogue record

Date deposited: 25 Aug 2026 16:31
Last modified: 13 Sep 2026 15:50

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Contributors

Author: Tseleung So
Author: Donald Stanley
Author: Stephen Theriault ORCID iD
Author: Ben Williams

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