Abstract
In this paper, we show that every closed, locally homogeneous Riemannian manifold with positive simplicial volume must be homeomorphic to a locally symmetric space of non-compact type, giving a converse to a result by Lafont and Schmidt within the scope of closed, locally homogeneous Riemannian manifolds. This characterizes all closed locally homogeneous Riemannian manifolds with nonzero simplicial volume.
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