Flat cycles in the homology of locally symmetric spaces covered by SL(n,R)/SO(n)

Locally symmetric spaces that are quotients of SL(n,R)/SO(n) by a lattice always have immersed, totally geodesic, flat tori of dimension (n-1). These tori are natural candidates for nontrivial homology cycles. We will explain how some of these (n-1)-dim tori give nontrivial rational homology cycles in congruence covers of SL(n,Z) \SL(n,R)/SO(n) and in Gamma\SL(n,R)/SO(n) for some cocompact lattices Gamma in SL(n,R).