 Solution

ID: past-exam-of-the-topology-and-groups-and-algebraic-topology-course-of-the-university-of-oxford/2007/b/8/iii/solution

Yes: for

n \geq 1

S^{n}

is connected, closed and oriented, with

H_{0} = H_{n} = 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.

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