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Hyperplane sections in arithmetic hyperbolic manifolds

2011; Wiley; Volume: 83; Issue: 2 Linguagem: Inglês

10.1112/jlms/jdq082

1469-7750

Nicolas Bergeron, Frédéric Haglund, Daniel T. Wise,

Advanced Algebra and Geometry

We prove that the fundamental groups of 'standard' arithmetic hyperbolic manifolds virtually retract onto their geometrically finite subgroups. In particular, this implies that the homology groups of immersed totally geodesic hypersurfaces of compact arithmetic hyperbolic manifolds virtually inject in the homology groups of the ambient manifold.