The splitting of the de Rham cohomology of soft function algebras is multiplicative
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910981303566336 |
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| author | Baskov, Igor |
| author_facet | Baskov, Igor |
| contents | Let $A$ be a real soft function algebra. In arXiv:2208.11431 we have obtained a canonical splitting $\mathrm{H}^* (Ω^\bullet _{A|\mathrm{R}}) \cong \mathrm{H} ^* (X,\mathrm{R})\oplus \text{(something)}$ via the canonical maps $Λ_A:\mathrm{H} ^* (X,\mathrm{R})\to\mathrm{H} ^* (Ω^\bullet _{A|\mathrm{R}})$ and $Ψ_A:\mathrm{H} ^* (Ω^\bullet _{A|\mathrm{R}})\to\mathrm{H} ^* (X,\mathrm{R})$. In this paper we prove that these maps are multiplicative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08689 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The splitting of the de Rham cohomology of soft function algebras is multiplicative Baskov, Igor Algebraic Topology Commutative Algebra Let $A$ be a real soft function algebra. In arXiv:2208.11431 we have obtained a canonical splitting $\mathrm{H}^* (Ω^\bullet _{A|\mathrm{R}}) \cong \mathrm{H} ^* (X,\mathrm{R})\oplus \text{(something)}$ via the canonical maps $Λ_A:\mathrm{H} ^* (X,\mathrm{R})\to\mathrm{H} ^* (Ω^\bullet _{A|\mathrm{R}})$ and $Ψ_A:\mathrm{H} ^* (Ω^\bullet _{A|\mathrm{R}})\to\mathrm{H} ^* (X,\mathrm{R})$. In this paper we prove that these maps are multiplicative. |
| title | The splitting of the de Rham cohomology of soft function algebras is multiplicative |
| topic | Algebraic Topology Commutative Algebra |
| url | https://arxiv.org/abs/2408.08689 |