Journal of Differential Geometry

Compactifications of symmetric spaces

A. Borel and L. Ji

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Compactifications of symmetric spaces have been constructed by different methods for various applications. One application is to provide the so-called rational boundary components which can be used to compactify locally symmetric spaces. In this paper, we construct many compactifications of symmetric spaces using a uniform method, which is motivated by the Borel-Serre compactification of locally symmetric spaces. Besides unifying compactifications of both symmetric and locally symmetric spaces, this uniform construction allows one to compare and relate easily different compactifications, to extend the group action continuously to boundaries of compactifications, and to clarify the structure of the boundaries.

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J. Differential Geom., Volume 75, Number 1 (2007), 1-56.

First available in Project Euclid: 30 March 2007

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Borel, A.; Ji, L. Compactifications of symmetric spaces. J. Differential Geom. 75 (2007), no. 1, 1--56. doi:10.4310/jdg/1175266253.

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