Surface Subgroups for Cocompact Lattices of Isometries of $H^{2n}$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909901267140608 |
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| author | Kahn, Jeremy Rao, Zhenghao |
| author_facet | Kahn, Jeremy Rao, Zhenghao |
| contents | We prove the existence of surface subgroups within any cocompact lattice $Γ$ in $\mathrm{SO}(2n,1)$ for $n\geq2$. This result addresses the cases missing from the work of Hamenstädt in 2015, who constructed surface subgroups in cocompact lattices for all other rank-one semisimple Lie groups of non-compact type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20759 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Surface Subgroups for Cocompact Lattices of Isometries of $H^{2n}$ Kahn, Jeremy Rao, Zhenghao Geometric Topology 22E40, 30F40 We prove the existence of surface subgroups within any cocompact lattice $Γ$ in $\mathrm{SO}(2n,1)$ for $n\geq2$. This result addresses the cases missing from the work of Hamenstädt in 2015, who constructed surface subgroups in cocompact lattices for all other rank-one semisimple Lie groups of non-compact type. |
| title | Surface Subgroups for Cocompact Lattices of Isometries of $H^{2n}$ |
| topic | Geometric Topology 22E40, 30F40 |
| url | https://arxiv.org/abs/2503.20759 |