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Mar 4, 2015 at 13:30 comment added Matthias Wendt A detailed discussion of the relation between the compactifications can be found in the book of Borel and Ji (Section III.15). In the case $SL_2\mathbb{Z}$, the boundary $S^1$ of the Borel-Serre compactification is mapped to the cusp point of the geodesic compactification. In the higher rank situations, the Borel-Serre compactification still has the geodesic compactification as a quotient, but I am not sure about the fibers.
Mar 1, 2015 at 13:23 comment added Spencer Leslie Thank you! Is there a way of understanding a relationship between the two compactifications you mention?
Mar 1, 2015 at 13:22 vote accept Spencer Leslie
Feb 28, 2015 at 12:32 history answered Matthias Wendt CC BY-SA 3.0