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In the process of attaching a $k$-Handle to a Manifold $M$, the Boundary of $M$ is modified by a process called $(k-1)$-surgery. Surgery consists of the removal of a Tubular Neighborhood of a $(k-1)$-Sphere $\Bbb{S}^{k-1}$ from the Boundaries of $M$ and the $\dim(M)-1$ 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

© 1996-9 Eric W. Weisstein