On the computation of $\mathrm{Ext}_{\mathcal A}^{k,k+*}(\mathbb{Z}/2,\mathbb{Z}/2)$ for $k \leq 5$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914043908849664 |
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| author | Phuc, Dang Vo |
| author_facet | Phuc, Dang Vo |
| contents | This Note presents a computational algorithm for determining a basis of the cohomology of the mod 2 Steenrod algebra, $\mathrm{Ext}_{\mathcal A}^{k, k+*}(\mathbb{Z}/2, \mathbb{Z}/2)$ for $k \leq 5$, based on the well-known generators and the Adams relations given in Chen's work [2]. The purpose of this algorithm is to verify the hand-computed results for $\mathrm{Ext}_{\mathcal A}^{4, 4+*}(\mathbb{Z}/2, \mathbb{Z}/2)$ presented in our corrected papers [8, 9, 10]. Combining our most recent works [11, 12], the verification of the domain and the codomain of the fourth algebraic transfer in specific degrees can now be completed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the computation of $\mathrm{Ext}_{\mathcal A}^{k,k+*}(\mathbb{Z}/2,\mathbb{Z}/2)$ for $k \leq 5$ Phuc, Dang Vo Algebraic Topology Geometric Topology Rings and Algebras 55T15, 55S10, 55S05 This Note presents a computational algorithm for determining a basis of the cohomology of the mod 2 Steenrod algebra, $\mathrm{Ext}_{\mathcal A}^{k, k+*}(\mathbb{Z}/2, \mathbb{Z}/2)$ for $k \leq 5$, based on the well-known generators and the Adams relations given in Chen's work [2]. The purpose of this algorithm is to verify the hand-computed results for $\mathrm{Ext}_{\mathcal A}^{4, 4+*}(\mathbb{Z}/2, \mathbb{Z}/2)$ presented in our corrected papers [8, 9, 10]. Combining our most recent works [11, 12], the verification of the domain and the codomain of the fourth algebraic transfer in specific degrees can now be completed. |
| title | On the computation of $\mathrm{Ext}_{\mathcal A}^{k,k+*}(\mathbb{Z}/2,\mathbb{Z}/2)$ for $k \leq 5$ |
| topic | Algebraic Topology Geometric Topology Rings and Algebras 55T15, 55S10, 55S05 |
| url | https://arxiv.org/abs/2507.15611 |