Steenrod closed parameter ideals in the mod-$2$ cohomology of $A_4$ and $SO(3)$
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866929713779310592 |
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| author | Rüping, Henrik Stephan, Marc Yalcin, Ergun |
| author_facet | Rüping, Henrik Stephan, Marc Yalcin, Ergun |
| contents | In this paper, we classify the parameter ideals in $H^*(BA_4;\mathbb{F}_2)$ and in the Dickson algebra $H^*(BSO(3);\mathbb{F}_2)$ that are closed under Steenrod operations. Consequently, we obtain restrictions on the dimensions $n,m$ for which $A_4$ (and $SO(3)$) can act freely on $S^n\times S^m$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2206_11802 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Steenrod closed parameter ideals in the mod-$2$ cohomology of $A_4$ and $SO(3)$ Rüping, Henrik Stephan, Marc Yalcin, Ergun Algebraic Topology Commutative Algebra 55M35 (Primary) 13C05, 55S10, 57S17, 20J06 (Secondary) In this paper, we classify the parameter ideals in $H^*(BA_4;\mathbb{F}_2)$ and in the Dickson algebra $H^*(BSO(3);\mathbb{F}_2)$ that are closed under Steenrod operations. Consequently, we obtain restrictions on the dimensions $n,m$ for which $A_4$ (and $SO(3)$) can act freely on $S^n\times S^m$. |
| title | Steenrod closed parameter ideals in the mod-$2$ cohomology of $A_4$ and $SO(3)$ |
| topic | Algebraic Topology Commutative Algebra 55M35 (Primary) 13C05, 55S10, 57S17, 20J06 (Secondary) |
| url | https://arxiv.org/abs/2206.11802 |