In the process of attaching a -Handle to a Manifold , the Boundary of is modified by a process called -surgery. Surgery consists of the removal of a Tubular Neighborhood of a -Sphere from the Boundaries of and the standard Sphere, and the gluing together of these two scarred-up objects along their common Boundaries.
See also Boundary, Dehn Surgery, Handle, Manifold, Sphere, Tubular Neighborhood