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In geometric topology, surgery theory is used to produce one finite-dimensional manifold from another in a 'controlled' way. Originally developed for differentiable (smooth) manifolds, surgery techniques also apply to piecewise linear and topological manifolds. Surgery refers to cutting out parts of the manifold and replacing it with a part of another manifold, matching up along the cut or boundary. This is related to handlebody decompositions.

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Does the coefficient of the meridian determine the coefficient of the longitude?(on Dehn sur...

It is almost 10 years old question but anyway: Let us glue only the meridian disk contained in our solid torus with respect to the coefficient. What remains to glue is a 3-ball, but since the mapping …
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