English

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.

Keywords

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

R2 v1 2026-07-01T07:48:15.132Z