About: Obstruction theory

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In mathematics, obstruction theory is a name given to two different mathematical theories, both of which yield cohomological invariants. In the original work of Stiefel and Whitney, characteristic classes were defined as obstructions to the existence of certain fields of linear independent vectors. Obstruction theory turns out to be an application of cohomology theory to the problem of constructing a cross-section of a bundle.

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rdfs:label	Obstruktionstheorie (de) Teoría de la obstrucción (es) Théorie de l'obstruction (fr) Obstruction theory (en) 阻碍理论 (zh)
rdfs:comment	In der Topologie, einem Teilgebiet der Mathematik, beschreibt die Obstruktionstheorie oder Hindernistheorie die Hindernisse für die Existenz von Schnitten in Faserbündeln. (de) La teoría de la obstrucción es una herramienta en topología algebraica y teoría de la homotopía que permite estudiar el problema de extender aplicación de un subespacio al espacio total. Esto en particular aplica al estudio del espacio de clases de homotopía de aplicación entre dos espacios. Análogamente permite estudiar cuando un par de aplicaciones son homótopas. Las clases características que aparecen en la teoría de fibrados se pueden entender como clases de obstrucción dotándolas de un significado geométrico. (es) En mathématiques, la théorie de l'obstruction est le nom donné en fait à plusieurs théories topologiques distinctes dont le but est de déterminer des invariants cohomologiques. (fr) In mathematics, obstruction theory is a name given to two different mathematical theories, both of which yield cohomological invariants. In the original work of Stiefel and Whitney, characteristic classes were defined as obstructions to the existence of certain fields of linear independent vectors. Obstruction theory turns out to be an application of cohomology theory to the problem of constructing a cross-section of a bundle. (en) 在数学中，阻碍理论（obstruction theory）是两个不同数学理论的名字，两者都导出了上同调不变量。 (zh)
dcterms:subject	Surgery theory Differential topology Homotopy theory Theories
Wikipage page ID	2179639 (xsd:integer)
Wikipage revision ID	1013765406 (xsd:integer)
Link from a Wikipage to another Wikipage	Samuel Eilenberg Homotopy equivalence Characteristic class Vector field Invariant (mathematics) L-theory Continuous mapping Surgery theory Mathematics Geometric topology Normal invariant N-skeleton N-sphere Contractible space Simplicial homology Homotopic Homotopy equivalent Poincaré duality Wall's finiteness obstruction Differential topology Eduard Stiefel Fiber bundle Diffeomorphism Differential structure Simplicial complex Postnikov system Homotopy theory Hassler Whitney Topological K-theory Theories Surgery theory Cohomology Homotopy fiber Homotopy group Homotopy theory Manifold CW complex Fibration Kirby–Siebenmann class Mathematical theory Topological manifold Section (fiber bundle) Vector bundle Principal bundle Simply connected Piecewise linear structure Path-connected Cohomological Cohomology group 0-skeleton
sameAs	Obstruction theory Obstruction theory Obstruction theory Obstruction theory Obstruction theory Obstruction theory Obstruction theory Obstruction theory
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has abstract	In der Topologie, einem Teilgebiet der Mathematik, beschreibt die Obstruktionstheorie oder Hindernistheorie die Hindernisse für die Existenz von Schnitten in Faserbündeln. (de) La teoría de la obstrucción es una herramienta en topología algebraica y teoría de la homotopía que permite estudiar el problema de extender aplicación de un subespacio al espacio total. Esto en particular aplica al estudio del espacio de clases de homotopía de aplicación entre dos espacios. Análogamente permite estudiar cuando un par de aplicaciones son homótopas. Las clases características que aparecen en la teoría de fibrados se pueden entender como clases de obstrucción dotándolas de un significado geométrico. (es) En mathématiques, la théorie de l'obstruction est le nom donné en fait à plusieurs théories topologiques distinctes dont le but est de déterminer des invariants cohomologiques. (fr) In mathematics, obstruction theory is a name given to two different mathematical theories, both of which yield cohomological invariants. In the original work of Stiefel and Whitney, characteristic classes were defined as obstructions to the existence of certain fields of linear independent vectors. Obstruction theory turns out to be an application of cohomology theory to the problem of constructing a cross-section of a bundle. (en) 在数学中，阻碍理论（obstruction theory）是两个不同数学理论的名字，两者都导出了上同调不变量。 (zh)
gold:hypernym	Name
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page length (characters) of wiki page	8288 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Obstruction_theory
is Link from a Wikipage to another Wikipage of	Projective representation Samuel Eilenberg List of algebraic topology topics Metaplectic structure

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