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Let $G$ be a discrete group and $BG$ some model for the classifying space of $G$. So $BG$ is an aspherical path-conected topological space.

Under which conditions is $BG$ a topological manifold or only homotopy equivalent to a topological manifold?

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# When is a classifying space a topological manifold?

Let $G$ be a discrete group and $BG$ some model for the classifying space of $G$. So $BG$ is an aspherical path-conected topological space.

Under which conditions is $BG$ a topological manifold?