What is "handlebody"

n. (context topology English) A top-dimensional submanifold of Euclidean space comprising a ball with handles attached to it along its boundary.

In the mathematical field of geometric topology, a handlebody is a decomposition of a manifold into standard pieces. Handlebodies play an important role in Morse theory, cobordism theory and the surgery theory of high-dimensional manifolds. Handles are used to particularly study 3-manifolds.

Handlebodies play a similar role in the study of manifolds as simplicial complexes and CW complexes play in homotopy theory, allowing one to analyze a space in terms of individual pieces and their interactions.