Steenrod operations for $4$-dimensional toric orbifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910894985838592 |
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| author | So, Tseleung |
| author_facet | So, Tseleung |
| contents | We prove necessary and sufficient conditions for the existence of non-trivial Steenrod actions on the mod-$2$ cohomology of 4-dimensional toric orbifolds. As applications, the stable homotopy type and the gauge groups of a $4$-dimensional toric orbifold are determined, a partial solution to the cohomological rigidity problem for $4$-dimensional toric orbifolds is provided, and, in the smooth case, a combinatorial criterion is established for when the toric orbifold is spin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Steenrod operations for $4$-dimensional toric orbifolds So, Tseleung Algebraic Topology Primary 55S10, 57S12, Secondary 57R18, 55P15 We prove necessary and sufficient conditions for the existence of non-trivial Steenrod actions on the mod-$2$ cohomology of 4-dimensional toric orbifolds. As applications, the stable homotopy type and the gauge groups of a $4$-dimensional toric orbifold are determined, a partial solution to the cohomological rigidity problem for $4$-dimensional toric orbifolds is provided, and, in the smooth case, a combinatorial criterion is established for when the toric orbifold is spin. |
| title | Steenrod operations for $4$-dimensional toric orbifolds |
| topic | Algebraic Topology Primary 55S10, 57S12, Secondary 57R18, 55P15 |
| url | https://arxiv.org/abs/2501.07907 |