Homology sphere
= Homology sphere
{wiki=Homology_sphere}
A homology sphere is a topological space that behaves like a sphere in terms of its homological properties, even if it is not actually a sphere in the classical sense. More formally, an \\( n \\)-dimensional homology sphere is a manifold that is homotopy equivalent to the \\( n \\)-dimensional sphere \\( S^n \\), and, importantly, it has the same homology groups as \\( S^n \\).