A note on relative Gelfand-Fuks cohomology of spheres
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910867410386944 |
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| author | Prigge, Nils |
| author_facet | Prigge, Nils |
| contents | We study the Gelfand-Fuks cohomology of smooth vector fields on $S^d$ relative to $\mathrm{SO}(d+1)$ following a method by Haefliger that uses tools from rational homotopy theory. In particular, we show that $H^*(\mathrm{BSO}(4);\mathbb{R})$ injects into the relative Gelfand-Fuks cohomology which corrects a claim by Haefliger. Moreover, for $S^3$ the relative Gelfand-Fuks cohomology agrees with the smooth cohomology of $\text{Diff}^+(S^3)$ and we provide a computation in low degrees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07322 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on relative Gelfand-Fuks cohomology of spheres Prigge, Nils Algebraic Topology 57R32 We study the Gelfand-Fuks cohomology of smooth vector fields on $S^d$ relative to $\mathrm{SO}(d+1)$ following a method by Haefliger that uses tools from rational homotopy theory. In particular, we show that $H^*(\mathrm{BSO}(4);\mathbb{R})$ injects into the relative Gelfand-Fuks cohomology which corrects a claim by Haefliger. Moreover, for $S^3$ the relative Gelfand-Fuks cohomology agrees with the smooth cohomology of $\text{Diff}^+(S^3)$ and we provide a computation in low degrees. |
| title | A note on relative Gelfand-Fuks cohomology of spheres |
| topic | Algebraic Topology 57R32 |
| url | https://arxiv.org/abs/2503.07322 |