Flat cycles in the homology of \Gamma \SL(m,R)/SO(m)
  In this paper we show that flat (m-1)-dimensional tori give nontrivial rational homology cycles in congruence covers of the locally symmetric space SL(m,Z) \SL(m,R)/SO(m). We also show that the dimension of the subspace of H_{m-1}(\Gamma \SL(m,R)/SO(m);Q) spanned by flat (m-1)-tori grows as one goes up in congruence covers. 
Grigori Avramidi, T. Tam Nguyen Phan
math.GT