Homotopy sphere

A **homotopy sphere** is a mathematical concept in the field of topology, specifically in geometric topology. It refers to a manifold that is homotopically equivalent to a sphere. This means that, while a homotopy sphere may not be geometrically the same as a standard sphere (such as the 2-sphere \( S^2 \) in three-dimensional space), it shares the same topological properties related to how paths can be continuously deformed within it.