  We show there exists a closed locally symmetric manifold $M$ modeled on
$SL_n(\mathbb R)/SO(n)$, and a non-trivial homology class in degree
$dim(M)-rank(M)$ represented by a totally geodesic submanifold that contains a
circle factor. As a result, the comparison map $c^k:H_b^k(M,\mathbb
R)\rightarrow H^k(M,\mathbb R)$ is not surjective in degree $k=dim(M)-rank(M)$.
This provides a counterpart to a result of Lafont-Wang which states that $c^k$
is always surjective in degree $k\geq dim(M)-rank(M)+2$.

Geometric Topology;Differential Geometry;Number Theory