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Results tagged with surgery-theory
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user 31475
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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Obtain 4-manifolds by repeating surgeries of submanifolds in $S^4$
It is a theorem of Iwase that every 4-manifold can be obtained from a connected sum of a number of $\pm CP^2$ and $S^1\times B^3$ by surgery along tori:
Iwase, Dehn surgery along a torus T2-knot II, …
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