Totally elliptic surface group representations
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913787055964160 |
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| author | Maret, Arnaud |
| author_facet | Maret, Arnaud |
| contents | A surface group representation into a Lie group is called totally elliptic if every simple closed curve on the surface is mapped to an elliptic element of the target group. In this note, we characterize all totally elliptic surface group representations into $\mathrm{PSL}_2\mathbb{R}$ and $\mathrm{PSL}_2\mathbb{C}$ by showing that they are either representations into a compact subgroup or Deroin--Tholozan representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19748 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Totally elliptic surface group representations Maret, Arnaud Representation Theory Group Theory Geometric Topology 57K20, 20C15 A surface group representation into a Lie group is called totally elliptic if every simple closed curve on the surface is mapped to an elliptic element of the target group. In this note, we characterize all totally elliptic surface group representations into $\mathrm{PSL}_2\mathbb{R}$ and $\mathrm{PSL}_2\mathbb{C}$ by showing that they are either representations into a compact subgroup or Deroin--Tholozan representations. |
| title | Totally elliptic surface group representations |
| topic | Representation Theory Group Theory Geometric Topology 57K20, 20C15 |
| url | https://arxiv.org/abs/2411.19748 |