Classifying space
http://dbpedia.org/resource/Classifying_space an entity of type: AnimalTissue105267548
In der Mathematik werden mit Hilfe des klassifizierenden Raumes und des universellen Bündels einer topologischen Gruppe G die Prinzipalbündel mit G als Strukturgruppe klassifiziert. Der klassifizierende Raum und das universelle Bündel sind durch eine universelle Eigenschaft charakterisiert, eine explizite Konstruktion geht auf John Milnor zurück. Bündel und ihre Klassifikation spielen eine wichtige Rolle in Mathematik und Theoretischer Physik.
rdf:langString
数学、特にホモトピー論では、位相群 G の分類空間(classifying space) BG は、G のにより空間 EG の商空間である（つまり、すべてのホモトピー群が自明となるような位相空間）。分類空間は、パラコンパクトな多様体上の任意の G 主バンドルが、主バンドル EG → BG の(pullback bundle)と同型となる性質を持つ。 離散群(discrete group) G に対し、BG は、大まかには、弧状連結な位相空間 X であり、X の基本群が G と同型となり、X の高次ホモトピー群が自明となる、つまり、BG は(Eilenberg-Maclane space)、または K(G,1) となる。
rdf:langString
대수적 위상수학에서 분류 공간(分流空間, 영어: classifying space)는 어떤 위상군을 올로 하는 모든 주다발들을 호모토피류들로 나타낼 수 있는 올다발이다.
rdf:langString
Em matemática, especificamente em teoria da homotopia, um espaço de classificação BG de um grupo topológico G é o quociente de um espaço EG (i.e. um espaço topológico para o qual todos seus são triviais) por uma de G. Tem a propriedade que qualquer fibrado principal G sobre uma variedade paracompacta ser isomórfica a uma do fibrado principal Para um G, BG é, grosseiramente falando, um espaço topológico de caminho ligado X tal que o grupo fundamental de X é isomórfico a G e os mais altos grupos de homotopia de X são .
rdf:langString
In mathematics, specifically in homotopy theory, a classifying space BG of a topological group G is the quotient of a weakly contractible space EG (i.e. a topological space all of whose homotopy groups are trivial) by a proper free action of G. It has the property that any G principal bundle over a paracompact manifold is isomorphic to a pullback of the principal bundle EG → BG. As explained later, this means that classifying spaces represent a set-valued functor on the homotopy category of topological spaces. The term classifying space can also be used for spaces that represent a set-valued functor on the category of topological spaces, such as Sierpiński space. This notion is generalized by the notion of classifying topos. However, the rest of this article discusses the more commonly use
rdf:langString
En mathématiques, un espace classifiant pour un groupe topologique G est la base d’un fibré principal particulier EG → BG appelé fibré universel, induisant tous les fibrés ayant ce groupe de structure sur n’importe quel CW-complexe X par image réciproque (pullback). Dans le cas d’un groupe discret, la définition d’espace classifiant correspond à celle d’un espace d'Eilenberg-MacLane K(G, 1), c’est-à-dire un espace connexe par arcs dont tous les groupes d'homotopie sont triviaux en dehors du groupe fondamental (lequel est isomorphe à G).
* Portail des mathématiques
rdf:langString
rdf:langString
Classifying space
rdf:langString
Klassifizierender Raum
rdf:langString
Espace classifiant
rdf:langString
분류 공간
rdf:langString
分類空間
rdf:langString
Espaço de classificação
xsd:integer
923556
xsd:integer
1111031167
rdf:langString
C/c022440
rdf:langString
classifying+space
rdf:langString
Classifying space
rdf:langString
In der Mathematik werden mit Hilfe des klassifizierenden Raumes und des universellen Bündels einer topologischen Gruppe G die Prinzipalbündel mit G als Strukturgruppe klassifiziert. Der klassifizierende Raum und das universelle Bündel sind durch eine universelle Eigenschaft charakterisiert, eine explizite Konstruktion geht auf John Milnor zurück. Bündel und ihre Klassifikation spielen eine wichtige Rolle in Mathematik und Theoretischer Physik.
rdf:langString
In mathematics, specifically in homotopy theory, a classifying space BG of a topological group G is the quotient of a weakly contractible space EG (i.e. a topological space all of whose homotopy groups are trivial) by a proper free action of G. It has the property that any G principal bundle over a paracompact manifold is isomorphic to a pullback of the principal bundle EG → BG. As explained later, this means that classifying spaces represent a set-valued functor on the homotopy category of topological spaces. The term classifying space can also be used for spaces that represent a set-valued functor on the category of topological spaces, such as Sierpiński space. This notion is generalized by the notion of classifying topos. However, the rest of this article discusses the more commonly used notion of classifying space up to homotopy. For a discrete group G, BG is, roughly speaking, a path-connected topological space X such that the fundamental group of X is isomorphic to G and the higher homotopy groups of X are trivial, that is, BG is an Eilenberg–MacLane space, or a K(G,1).
rdf:langString
En mathématiques, un espace classifiant pour un groupe topologique G est la base d’un fibré principal particulier EG → BG appelé fibré universel, induisant tous les fibrés ayant ce groupe de structure sur n’importe quel CW-complexe X par image réciproque (pullback). Dans le cas d’un groupe discret, la définition d’espace classifiant correspond à celle d’un espace d'Eilenberg-MacLane K(G, 1), c’est-à-dire un espace connexe par arcs dont tous les groupes d'homotopie sont triviaux en dehors du groupe fondamental (lequel est isomorphe à G). La notion s’étend avec celle d’espace classifiant d’une catégorie, qui est une réalisation géométrique de son nerf.
* Portail des mathématiques
rdf:langString
数学、特にホモトピー論では、位相群 G の分類空間(classifying space) BG は、G のにより空間 EG の商空間である（つまり、すべてのホモトピー群が自明となるような位相空間）。分類空間は、パラコンパクトな多様体上の任意の G 主バンドルが、主バンドル EG → BG の(pullback bundle)と同型となる性質を持つ。 離散群(discrete group) G に対し、BG は、大まかには、弧状連結な位相空間 X であり、X の基本群が G と同型となり、X の高次ホモトピー群が自明となる、つまり、BG は(Eilenberg-Maclane space)、または K(G,1) となる。
rdf:langString
대수적 위상수학에서 분류 공간(分流空間, 영어: classifying space)는 어떤 위상군을 올로 하는 모든 주다발들을 호모토피류들로 나타낼 수 있는 올다발이다.
rdf:langString
Em matemática, especificamente em teoria da homotopia, um espaço de classificação BG de um grupo topológico G é o quociente de um espaço EG (i.e. um espaço topológico para o qual todos seus são triviais) por uma de G. Tem a propriedade que qualquer fibrado principal G sobre uma variedade paracompacta ser isomórfica a uma do fibrado principal Para um G, BG é, grosseiramente falando, um espaço topológico de caminho ligado X tal que o grupo fundamental de X é isomórfico a G e os mais altos grupos de homotopia de X são .
xsd:nonNegativeInteger
12422