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Surface Subgroups for Cocompact Lattices of Isometries of $H^{2n}$
Published 26 Mar 2025 in math.GT | (2503.20759v3)
Abstract: We prove the existence of surface subgroups within any cocompact lattice $\Gamma$ in $\mathrm{SO}(2n,1)$ for $n\geq2$. This result addresses the cases missing from the work of Hamenst\"adt 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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