TITLE: How to prove the connected sum of two closed aspherical n-manfolds (n >2) is not asperical?
QUESTION [9 upvotes]: The intuitive idea is that the sphere connected the two manifolds is not contractible, which implies the (n-1)th homotopy group is not zero. Another argument, which I am not totally understand, uses the fact that the universal covering of an aspherical manifold has only one end. I am wondering if someone here could clarify these for me or give me a new argument.

REPLY [4 votes]: Darryl McCullough gives a very complete answer to your question in his "Connected Sums of Aspherical Manifolds" paper. Let  $M$ be the connected sum of $g$ aspherical manifolds of dimension $d\geq 3$. Its universal cover $\tilde M$ is homotopy equivalent to $\bigvee_{\rho \in \pi_1(M)} \bigvee_{i=1}^{g-1}S^{d-1}$ (and in particular is not contractible). 
I wonder if there is a short proof of this along the lines of Robert Bell's answer.