In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one manifold from another in a 'controlled' way, introduced by Milnor (1961). 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 closely related to, but not identical with, handlebody decompositions. It is a major tool in the study and classification of manifolds of dimension greater than 4.
More technically, the idea is to start with a well-understood manifold M and perform surgery on it to produce a manifold M ′ having some desired property, in such a way that the effects on the homology, homotopy groups, or other interesting invariants of the manifold are known.
The classification of exotic spheres by Kervaire and Milnor (1963) led to the emergence of surgery theory as a major tool in high-dimensional topology.
Read more about Surgery Theory: Surgery On A Manifold, Application To Classification of Manifolds, See Also
Famous quotes containing the words surgery and/or theory:
“Ever since surgery began, man’s destiny has been to suffer, in order that he might be cured. And no one can change that, gentlemen.”
—Jean Scott Rogers. Robert Day. Mr. Blount (Frank Pettingell)
“No one thinks anything silly is suitable when they are an adolescent. Such an enormous share of their own behavior is silly that they lose all proper perspective on silliness, like a baker who is nauseated by the sight of his own eclairs. This provides another good argument for the emerging theory that the best use of cryogenics is to freeze all human beings when they are between the ages of twelve and nineteen.”
—Anna Quindlen (20th century)