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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.11235 |
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| _version_ | 1866911315639926784 |
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| author | Bao, Allen Chakraborty, Anunoy Duncan, David L. Larson, Jordan McBride, Kelson |
| author_facet | Bao, Allen Chakraborty, Anunoy Duncan, David L. Larson, Jordan McBride, Kelson |
| contents | We investigate the $G$-representation varieties of right-angled Artin groups (RAAGs) for various Lie groups $G$. We show these varieties are connected for a large class of such $G$, including $\mathrm{SU}(n), \mathrm{Sp}(n)$ and $\mathrm{U}(n)$, while they are generally not connected for other large classes, such as $\mathrm{SO}(n)$ and $\mathrm{Spin}(n)$ for $n \geq 3$. When $G = \mathrm{SO}(3)$ we determine the number of connected components of the representation variety associated to any RAAG that is also a 3-manifold group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11235 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representation varieties of RAAGs Bao, Allen Chakraborty, Anunoy Duncan, David L. Larson, Jordan McBride, Kelson Geometric Topology We investigate the $G$-representation varieties of right-angled Artin groups (RAAGs) for various Lie groups $G$. We show these varieties are connected for a large class of such $G$, including $\mathrm{SU}(n), \mathrm{Sp}(n)$ and $\mathrm{U}(n)$, while they are generally not connected for other large classes, such as $\mathrm{SO}(n)$ and $\mathrm{Spin}(n)$ for $n \geq 3$. When $G = \mathrm{SO}(3)$ we determine the number of connected components of the representation variety associated to any RAAG that is also a 3-manifold group. |
| title | Representation varieties of RAAGs |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2512.11235 |