Asian Journal of Mathematics

Volume 22 (2018)

Number 5

Fundamental groups of toroidal compactifications

Pages: 941 – 954



A. K. Kasparian (Faculty of Mathematics and Informatics, Kliment Ohridski University of Sofia, Bulgaria)

G. K. Sankaran (Department of Mathematical Sciences, University of Bath, England, United Kingdom)


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.


toroidal compactification, fundamental group, maximal parabolic subgroups

2010 Mathematics Subject Classification

14M27, 32M12, 55Q52, 57T15

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