nLab homology sphere

Idea

A homology sphere is a topological space which need not be homeomorphic to an n-sphere, but which has the same ordinary homology as an $n$-sphere.

Properties

Corollary

Every homology sphere is a rational homology sphere.

Corollary

Every homotopy sphere is a homology sphere.

Theorem

Every simply connected homology sphere is a homotopy sphere.

Proposition

There are simply connected homology-$n$-spheres not homeomorphic to the $n$-sphere iff $n\geq 5$.

Related concepts

• rational homology sphere
• homotopy sphere
• rational homotopy sphere

Redirects

• Wikipedia, Homology sphere