Handle decomposition is a concept often used in topology, particularly in the study of manifolds. It is a method for breaking down a manifold into simpler pieces, called "handles," that can be more easily analyzed and understood. In general terms, a handle is a type of topological feature that can be thought of as a "thickening" of a lower-dimensional manifold.
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A handle decomposition builds an -dimensional manifold by successively adjoining along . The attaching data comprise an attaching sphere and its framing of an embedded sphere. Reading a decomposition backwards replaces index by index and interchanges its attaching spheres and belt spheres.