Realizing orders in rational sphere product algebras with three generators
Rings and Algebras
2026-03-02 v1 Algebraic Topology
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 odd.
Cite
@article{arxiv.2511.16910,
title = {Realizing orders in rational sphere product algebras with three generators},
author = {Tseleung So and Donald Stanley and Stephen Theriault and Ben Williams},
journal= {arXiv preprint arXiv:2511.16910},
year = {2026}
}
Comments
23 pages