Journal of Differential Geometry

Compactifications of symmetric spaces

A. Borel and L. Ji

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 30 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1175266253

Digital Object Identifier
doi:10.4310/jdg/1175266253

Mathematical Reviews number (MathSciNet)
MR2282724

Zentralblatt MATH identifier
1110.53036

Citation

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


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