Abstract
Let M be a complete Riemannian manifold of bounded nonpositive sectional curvature and finite volume. We construct a topological Tits building Δ\(\tilde M\) associated to the universal cover of M. If M is irreducible and rank (M)≥2, we show that Δ\(\tilde M\) is a building canonically associated with a Lie group and hence that M is locally symmetric.
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Supported in part by NSF Grant MCS-82-04024 and M.S.R.I., Berkeley.
Supported in part by NSF Grant DMS-84-01760 and M.S.R.I., Berkeley.
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Burns, K., Spatzier, R. Manifolds of nonpositive curvature and their buildings. Publications Mathématiques de L’Institut des Hautes Scientifiques 65, 35–59 (1987). https://doi.org/10.1007/BF02698934
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DOI: https://doi.org/10.1007/BF02698934