What is "dehn surgery"

n. 1 (context topology English) The removal of a solid torus from a 3-dimensional manifold, followed by its being replaced via a homeomorphism of its boundary. 2 (context topology specifically English) The same, but with the manifold in question being the 3-dimensional sphere.

In topology, a branch of mathematics, a Dehn surgery, named after Max Dehn, is a construction used to modify 3-manifolds. The process takes as input a 3-manifold together with a link. It is often conceptualized as two steps: drilling then filling.