Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
The top dimensional cohomology of a connected manifold is non-zero if and only if the manifold is compact, so the answer is "yes" for homology spheres.
EDIT: As Mariano remarks below, "compact" should read "compact and orientable".
The top dimensional cohomology of a connected manifold is non-zero if and only if the manifold is compact, so the answer is "yes" for homology spheres.
The top dimensional cohomology of a connected manifold is non-zero if and only if the manifold is compact, so the answer is "yes" for homology spheres.
EDIT: As Mariano remarks below, "compact" should read "compact and orientable".
The top dimensional cohomology of a connected manifold is non-zero if and only if the manifold is compact, so the answer is "yes" for homology spheres.
