Surface Subgroups for Cocompact Lattices of Isometries of H2n
Abstract
We prove the existence of surface subgroups within any cocompact lattice in SO(2n,1) for n≥2. 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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