\b[Yes:] for $n\ge1$, the sphere $S^n$ is <connected>, closed and oriented, with $H_0=H_n=\mathbb Z$ and no intermediate <homology>. These groups do not require the <manifold> to be homeomorphic to a sphere, but the sphere provides the requested example.

Solution

Past exam of the topology and Groups and Algebraic Topology course of the University of Oxford / 2007 / B / 8 / iii / Solution

 Solution (source code)