A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry

Details A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry

2009-03-03

arxiv.org/abs/0903.0584v1

Mathematics

Metric Geometry

My 1997 habilitation thesis as published in Bonner Mathematische Schriften vol 326 (2000)

Scientific paper

We study geodesically complete and locally compact Hadamard spaces X whose Tits boundary is a connected irreducible spherical building. We show that X is symmetric iff complete geodesics in X do not branch and a Euclidean building otherwise. Furthermore, every boundary equivalence (cone topology homeomorphism preserving the Tits metric) between two such spaces is induced by a homothety. As an application, we can extend the Mostow and Prasad rigidity theorems to compact singular (orbi)spaces of nonpositive curvature which are homotopy equivalent to a quotient of a symmetric space or Euclidean building by a cocompact group of isometries.

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