Algebraic cohomotopy groups, algebraic fundamental groups and stably free modules
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908720199368704 |
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| author | Sridharan, Raja Upadhyay, Sumit Kumar |
| author_facet | Sridharan, Raja Upadhyay, Sumit Kumar |
| contents | In this article, we prove the algebraic counterpart of the topological results $H^1(S^1, \mathbb{Z}) \cong \mathbb{Z}$ and $H^1(S^2, \mathbb{Z}) \cong \{0\}$. We also see that a non-trivial element of the algebraic cohomotopy groups of certain rings associated with some known topological spaces provides examples of non-free stably free module of rank two over those rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16664 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebraic cohomotopy groups, algebraic fundamental groups and stably free modules Sridharan, Raja Upadhyay, Sumit Kumar Group Theory In this article, we prove the algebraic counterpart of the topological results $H^1(S^1, \mathbb{Z}) \cong \mathbb{Z}$ and $H^1(S^2, \mathbb{Z}) \cong \{0\}$. We also see that a non-trivial element of the algebraic cohomotopy groups of certain rings associated with some known topological spaces provides examples of non-free stably free module of rank two over those rings. |
| title | Algebraic cohomotopy groups, algebraic fundamental groups and stably free modules |
| topic | Group Theory |
| url | https://arxiv.org/abs/2512.16664 |