Classification of the topological holonomy groups in $SO(3)$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911392782614528 |
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| author | Ando, Naoya |
| author_facet | Ando, Naoya |
| contents | In this paper, we obtain classification of the topological holonomy groups in $SO(3)$. Such a group is given by one of the following: a finite group (such groups are classified by Klein); a commutative infinite group which is generated by one or two elements, and dense in a subgroup of $SO(3)$ isomorphic to $SO(2)$; a non-commutative infinite group generated by two elements of order $2$, $\infty$ such that these rotation axes are orthogonal; a non-commutative infinite group which is dense in $SO(3)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20593 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of the topological holonomy groups in $SO(3)$ Ando, Naoya Differential Geometry In this paper, we obtain classification of the topological holonomy groups in $SO(3)$. Such a group is given by one of the following: a finite group (such groups are classified by Klein); a commutative infinite group which is generated by one or two elements, and dense in a subgroup of $SO(3)$ isomorphic to $SO(2)$; a non-commutative infinite group generated by two elements of order $2$, $\infty$ such that these rotation axes are orthogonal; a non-commutative infinite group which is dense in $SO(3)$. |
| title | Classification of the topological holonomy groups in $SO(3)$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2507.20593 |