About: Surgery theory

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In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by John Milnor. Milnor called this technique surgery, while Andrew Wallace called it spherical modification. The "surgery" on a differentiable manifold M of dimension , could be described as removing an imbedded sphere of dimension p from M. Originally developed for differentiable (or, smooth) manifolds, surgery techniques also apply to piecewise linear (PL-) and topological manifolds.

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rdf:type	Thing book
rdfs:label	Surgery theory (en) Chirurgie (Mathematik) (de) Chirurgie (topologie) (fr) 수술 (수학) (ko) Перестройка Морса (ru) 割補理論 (zh)
rdfs:comment	Chirurgie ist eine Methode in der Topologie von Mannigfaltigkeiten. Sie wurde von Milnor und Kervaire zur Klassifikation entwickelt und dann in Arbeiten von Browder, Nowikow, Sullivan und Wall zur Klassifikation höher-dimensionaler Mannigfaltigkeiten ausgebaut. Die Grundidee der Chirurgie an einer differenzierbaren Mannigfaltigkeit ist, aus einer -dimensionalen Mannigfaltigkeit mit Einbettung die Untermenge zu entfernen und an der Stelle mit zu ersetzen. Dadurch entsteht eine neue -dimensionale Mannigfaltigkeit wobei die Sphäre und die Kugel bezeichnet. (de) 미분위상수학에서 수술(手術, 영어: surgery 서저리[*])은 다양체 속의 원기둥을 도려내고 그 자리에 다른 모양의 원기둥을 붙여 전체의 위상을 바꾸는 연산이다. 수술은 고차원 (5차원 이상) 다양체의 연구에 매우 중요한 역할을 하며, 그 이론을 수술 이론(手術理論, 영어: surgery theory)이라고 한다. (ko) 在數學中，尤其是拓撲學，割補理論(surgery theory)是一種用於從另一流形對象產生一個有限維流形、並在「控制」之下的理論方法。其最初是用於處理光滑流形，之後陸續被應用於以及拓撲流形等等。 (zh) En mathématiques, et particulièrement en topologie géométrique, la chirurgie est une technique, introduite en 1961 par John Milnor, permettant de construire une variété à partir d'une autre de manière « contrôlée ». On parle de chirurgie parce que cela consiste à « couper » une partie de la première variété et à la remplacer par une partie d'une autre variété, en identifiant les frontières ; ces transformations sont étroitement liées à la notion de décomposition en anses. La chirurgie est un outil essentiel dans l'étude et la classification des variétés de dimension supérieure à 4. (fr) In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by John Milnor. Milnor called this technique surgery, while Andrew Wallace called it spherical modification. The "surgery" on a differentiable manifold M of dimension , could be described as removing an imbedded sphere of dimension p from M. Originally developed for differentiable (or, smooth) manifolds, surgery techniques also apply to piecewise linear (PL-) and topological manifolds. (en) Хирургия или перестройка Морса — преобразование гладких многообразий, которому подвергается многообразие уровня гладкой функции при переходе через невырожденную критическую точку; важнейшая конструкция в дифференциальной топологии. (ru)
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dcterms:subject	Surgery theory
Wikipage page ID	5961115 (xsd:integer)
Wikipage revision ID	1103433772 (xsd:integer)
Link from a Wikipage to another Wikipage	Princeton University Press Scalar curvature Proceedings of the London Mathematical Society Dennis Sullivan Andrew H. Wallace Annals of Mathematics Homotopy equivalence Hyperbolic group Dehn surgery L-theory Thom space Surgery obstruction Surgery theory Mathematics Geometric topology Normal bundle Obstruction theory Orientation character Morse theory Homotopic Stable vector bundle Complete set of invariants Embedding C. T. C. Wall Torus William Browder (mathematician) Laurent C. Siebenmann Poincaré duality American Mathematical Society Exotic sphere Diffeomorphism Handlebody Manifold decomposition Cobordism Codimension Cohomology Homeomorphism Homology (mathematics) Homotopy Homotopy group Whitehead torsion Differentiable manifold Assembly map Manifold Borel conjecture Piecewise linear manifold Sphere Classification of manifolds Group ring H-cobordism theorem Klein bottle Sergei Novikov (mathematician) Topological manifold Signature Surgery exact sequence Differentiable manifolds Plumbing (mathematics) Poincaré complex Surgery structure set Normal invariants Morse function Bordism Springer-Verlag S-cobordism theorem Fibration sequence Spectrum (homotopy theory) dbr:Spivak_normal_fibration
Link from a Wikipage to an external page	http://www.map.mpim-bonn.mpg.de http://www.maths.ed.ac.uk/~aar/books/scm.pdf http://www.math.harvard.edu/~lurie/287x.html http://www.maths.ed.ac.uk/~aar/ http://www.maths.ed.ac.uk/~aar/books/wall1.pdf http://www.maths.ed.ac.uk/~aar/books/wall2.pdf http://www.maths.ed.ac.uk/~aar/papers/lurie2011.pdf

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