Surgery Theory
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High Quality Content by WIKIPEDIA articles! In mathematics, specifically in topology, surgery theory is a collection of techniques used to produce one manifold from another in a 'controlled' way. 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. 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…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, specifically in topology, surgery theory is a collection of techniques used to produce one manifold from another in a 'controlled' way. 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. 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.