Handle (mathematics)

In topology, a branch of mathematics, a handle is just a topological ball; it is called a handle because of the context in which it is discussed, of which there are two: handle decompositions and handlebodies.

A handle is a subset of a manifold which is one of the components of a handle decomposition of the manifold,

A handle is a subset of a handlebody with the topology of a ball, which may be cut along a 2-disk so as to reduce the genus of the handlebody; a handlebody of genus n will have n handles.