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arXiv · 2503.20759

Surface Subgroups for Cocompact Lattices of Isometries of $H^{2n}$

Jeremy Kahn·Zhenghao Rao
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Abstract

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.

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Jeremy Kahn, Zhenghao Rao. 2025-11-14. Surface Subgroups for Cocompact Lattices of Isometries of $H^{2n}$. https://doi.org/10.1112/topo.70089

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