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Geometry of compactifications of locally symmetric spaces

Lizhen JiRobert Macpherson — 2002

Annales de l’institut Fourier

For a locally symmetric space M , we define a compactification M M ( ) which we call the “geodesic compactification”. It is constructed by adding limit points in M ( ) to certain geodesics in M . The geodesic compactification arises in other contexts. Two general constructions of Gromov for an ideal boundary of a Riemannian manifold give M ( ) for locally symmetric spaces. Moreover, M ( ) has a natural group theoretic construction using the Tits building. The geodesic compactification plays two fundamental roles in...

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