Domination between non-Fuchsian representations and anti-de Sitter geometry
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908650689265664 |
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| author | Diaf, Farid Mesbah, Abderrahim Sagman, Nathaniel |
| author_facet | Diaf, Farid Mesbah, Abderrahim Sagman, Nathaniel |
| contents | Motivated by work of various authors on domination between surface group representations, harmonic maps, and $3$-dimensional anti-de Sitter geometry, we study a new domination problem between non-Fuchsian representations of closed surface groups. We solve the problem for representations that admit branched harmonic immersions, and we show that, outside of this case, the problem cannot always be solved. We then show that a dominating pair gives rise to an anti-de Sitter $3$-manifold with singularities, and we construct large families of branched anti-de Sitter $3$-manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10570 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Domination between non-Fuchsian representations and anti-de Sitter geometry Diaf, Farid Mesbah, Abderrahim Sagman, Nathaniel Differential Geometry Geometric Topology Motivated by work of various authors on domination between surface group representations, harmonic maps, and $3$-dimensional anti-de Sitter geometry, we study a new domination problem between non-Fuchsian representations of closed surface groups. We solve the problem for representations that admit branched harmonic immersions, and we show that, outside of this case, the problem cannot always be solved. We then show that a dominating pair gives rise to an anti-de Sitter $3$-manifold with singularities, and we construct large families of branched anti-de Sitter $3$-manifolds. |
| title | Domination between non-Fuchsian representations and anti-de Sitter geometry |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2511.10570 |