About: Thom space

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In mathematics, the Thom space, Thom complex, or Pontryagin–Thom construction (named after René Thom and Lev Pontryagin) of algebraic topology and differential topology is a topological space associated to a vector bundle, over any paracompact space.

Attributes	Values
rdf:type	yago:WikicatCharacteristicClasses yago:Abstraction100002137 yago:Class107997703 yago:Collection107951464 yago:Group100031264
rdfs:label	Thom-Raum (de) Espace de Thom (fr) 톰 공간 (ko) Thom space (en)
rdfs:comment	Der Thom-Raum oder Thom-Komplex, benannt nach René Thom, ist in der algebraischen Topologie und Differentialtopologie ein einem Vektorbündel zugeordneter topologischer Raum. (de) En topologie, l'espace de Thom est un espace topologique associé à un fibré vectoriel. Il est au cœur de plusieurs constructions homotopiques, parmi lesquelles la construction de Thom-Pontrjagin et le (en) de Thom. Il porte le nom de René Thom, qui a introduit ces constructions en 1954. (fr) In mathematics, the Thom space, Thom complex, or Pontryagin–Thom construction (named after René Thom and Lev Pontryagin) of algebraic topology and differential topology is a topological space associated to a vector bundle, over any paracompact space. (en) 대수적 위상수학에서 톰 공간(Thom空間, 영어: Thom space)은 실수 벡터 다발에 하나의 “무한대” 점을 추가하여 얻는 위상 공간이다. 이를 사용하여 미분위상수학의 일부 대상들을 호모토피 이론의 기법으로 다룰 수 있다. (ko)
dcterms:subject	Characteristic classes Algebraic topology
Wikipage page ID	1243451 (xsd:integer)
Wikipage revision ID	1089145577 (xsd:integer)
Link from a Wikipage to another Wikipage	Princeton University Press Algebraic topology Homotopy groups René Thom Ring isomorphism Characteristic classes Vector space List of important publications in mathematics Stiefel–Whitney class Transversality (mathematics) Mathematics Natural transformation Tangent bundle Orientation of a vector bundle Left-hand side and right-hand side of an equation Lev Pontryagin Stable homotopy groups of spheres Commentarii Mathematici Helvetici Spectrum (topology) Suspension (topology) MathOverflow Coefficients Hattori–Stong theorem Pointed space Poincaré duality Algebraic topology Fiber (mathematics) Fiber bundle Paracompact space Differential topology Journal of Topology Smash product Stable homotopy theory John Milnor Surgery theory Cobordism Cobordism ring Cohomology Cohomology operation Bulletin of the AMS Paracompact Identity (mathematics) Orientability Real number Sergei Novikov (mathematician) Topological manifold University of Chicago Press Vector bundle Euler class Transversality theorem Topological space Steenrod problem Universal vector bundle Sphere bundle Steenrod operation Oriented bundle Wu formula Reduced cohomology Smooth manifolds Pontryagin classes Spectrum (homotopy theory) Thom transversality theorem
Link from a Wikipage to an external page	http://ncatlab.org/nlab/show/Thom+spectrum https://mathoverflow.net/questions/7375/explanation-for-the-thom-pontryagin-construction-and-its-generalisations https://amathew.wordpress.com/tag/thom-space/
sameAs	Thom space Thom space Thom space Thom space Thom space Thom space Thom space
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Cite_book dbt:Cite_journal dbt:Cite_web dbt:Reflist dbt:Math_theorem
id	p/t092680 (en)
title	Thom space (en)
has abstract	Der Thom-Raum oder Thom-Komplex, benannt nach René Thom, ist in der algebraischen Topologie und Differentialtopologie ein einem Vektorbündel zugeordneter topologischer Raum. (de) En topologie, l'espace de Thom est un espace topologique associé à un fibré vectoriel. Il est au cœur de plusieurs constructions homotopiques, parmi lesquelles la construction de Thom-Pontrjagin et le (en) de Thom. Il porte le nom de René Thom, qui a introduit ces constructions en 1954. (fr) In mathematics, the Thom space, Thom complex, or Pontryagin–Thom construction (named after René Thom and Lev Pontryagin) of algebraic topology and differential topology is a topological space associated to a vector bundle, over any paracompact space. (en)

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