Cofinite proper classifying spaces for lattices in semisimple Lie groups of $mathbb R$-rank $1$

摘要

The Borel--Serre partial compactification gives cofinite models for the proper classifying space for arithmetic lattices. Non-arithmetic lattices arise only in semisimple Lie groups of $mathbb R$-rank one. The author generalizes the Borel--Serre partial compactification to construct cofinite models for the proper classifying space for lattices in semisimple Lie groups of $mathbb R$-rank one by using the reduction theory of Garland and Raghunathan.