The topological holonomy group and the complexity of horizontality
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918300308471808 |
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| author | Ando, Naoya Yonezaki, Anri |
| author_facet | Ando, Naoya Yonezaki, Anri |
| contents | Based on [1], we study the complexity of horizontality in each twistor space $\hat{E}_{\varepsilon}$ associated with an oriented vector bundle $E$ of rank $4$ with a positive-definite metric over the $2$-torus $T^2$, and obtain classification of the topological holonomy groups in $SO(3)$. We observe that there exist many topological holonomy groups in $SO(3)$ generated by two finite order elements and equipped with noncommutative pairs which consist of infinite order elements. We find topological holonomy groups which are dense in $SO(4)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_10092 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The topological holonomy group and the complexity of horizontality Ando, Naoya Yonezaki, Anri Differential Geometry Based on [1], we study the complexity of horizontality in each twistor space $\hat{E}_{\varepsilon}$ associated with an oriented vector bundle $E$ of rank $4$ with a positive-definite metric over the $2$-torus $T^2$, and obtain classification of the topological holonomy groups in $SO(3)$. We observe that there exist many topological holonomy groups in $SO(3)$ generated by two finite order elements and equipped with noncommutative pairs which consist of infinite order elements. We find topological holonomy groups which are dense in $SO(4)$. |
| title | The topological holonomy group and the complexity of horizontality |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2407.10092 |