Fundamental groups of toroidal compactifications

We compute the fundamental group of a toroidal compactification of a Hermitian locally symmetric space $D / \Gamma$, without assuming either that $\Gamma$ is neat or that it is arithmetic. We also give bounds for the first Betti number.

Keywords

toroidal compactification, fundamental group, maximal parabolic subgroups

2010 Mathematics Subject Classification

14M27, 32M12, 55Q52, 57T15

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The first author’s research was partially supported by Contract 015/9.04.2014 with the the Scientific Foundation of Kliment Ohridski University of Sofia.

Received 10 July 2015

Accepted 29 November 2016

Published 9 November 2018