Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2017; 32(3): 745-763

Online first article April 3, 2017      Printed July 31, 2017

https://doi.org/10.4134/CKMS.c160222

Copyright © The Korean Mathematical Society.

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

Hyosang Kang

DGIST

Abstract

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.

Keywords: partial compactification, reduction theory, Lattices in Lie groups, proper classifying spaces

MSC numbers: 57M60, 57S20, 57T20, 55R35

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