Dehn surgery is a concept in the field of 3-manifold topology, named after the mathematician Rudolf Dehn. It is a technique used to construct new 3-manifolds from a given 3-manifold by cutting along a torus and gluing back the resulting boundary in a specific way.
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Dehn surgery removes tubular neighborhoods of a link in a three-dimensional manifold and performs Dehn filling on their boundary tori with specified primitive meridian slopes. Dehn surgery on a framed link is the integral-slope special case.