A space $ X$ (by which I mean a CW complex) is acyclic if its reduced singular homology $ \tilde H_\ast(X;\Bbb Z)$ is trivial in all degrees.
A discrete group $ \pi$ is said to be acyclic if its classifying space $ B\pi$ is acyclic.
A space $ X$ is aspherical if its universal cover is contractible. A space $ X$ is non-aspherical if its universal cover isn’t contractible.
Question: Does there exist a non-aspherical, acyclic space $ X$ whose fundamental group $ \pi$ is also acyclic?
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