**Papers Published**

- Ji, L; Murty, VK; Saper, L; Scherk, J,
*The fundamental group of reductive Borel–Serre and Satake compactifications*, Asian Journal of Mathematics, vol. 19 no. 3 (2015), pp. 465-486, International Press of Boston

(last updated on 2022/05/21)**Abstract:**

Let G be an almost simple, simply connected algebraic group defined over a number field k, and let S be a finite set of places of k including all infinite places. Let X be the product over v ε S of the symmetric spaces associated to G(kv), when v is an infinite place, and the Bruhat-Tits buildings associated to G(kv), when v is a finite place. The main result of this paper is to compute explicitly the fundamental group of the reductive Borel-Serre compactification of Γ\X, where Γ is an S-arithmetic subgroup of G. In the case that G is neat, we show that this fundamental group is isomorphic to Γ/EΓ, where EΓ is the subgroup generated by the elements of Γ belonging to unipotent radicals of k-parabolic subgroups. Analogous computations of the fundamental group of the Satake compactifications are made. It is noteworthy that calculations of the congruence subgroup kernel C(S, G) yield similar results.