Realizing orders in rational sphere product algebras with three generators
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911472656842752 |
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| 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 |