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Manifolds of nonpositive curvature and their buildings

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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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Authors and Affiliations

  1. Department of Mathematics, Indiana University, 47405, Bloomington, IN, U.S.A.

    Keith Burns & Ralf Spatzier

  2. Department of Mathematics, S.U.N.Y. at Stony Brook, 11794, Stony Brook, NY, U.S.A.

    Keith Burns & Ralf Spatzier

Authors
  1. Keith Burns
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  2. Ralf Spatzier
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Additional information

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

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