Realizing orders in rational sphere product algebras with three generators

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: So, Tseleung, Stanley, Donald, Theriault, Stephen, Williams, Ben
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866911472656842752
author So, Tseleung
Stanley, Donald
Theriault, Stephen
Williams, Ben
author_facet So, Tseleung
Stanley, Donald
Theriault, Stephen
Williams, Ben
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_16910
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Realizing orders in rational sphere product algebras with three generators
So, Tseleung
Stanley, Donald
Theriault, Stephen
Williams, Ben
Rings and Algebras
Algebraic Topology
Primary 55N10 Secondary 13F55, 55P99, 55T20
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.
title Realizing orders in rational sphere product algebras with three generators
topic Rings and Algebras
Algebraic Topology
Primary 55N10 Secondary 13F55, 55P99, 55T20
url https://arxiv.org/abs/2511.16910