In mathematics, specifically in algebraic topology, the Eilenberg–Zilber theorem is an important result in establishing the link between the homology groups of a product space and those of the spaces and . The theorem first appeared in a 1953 paper in the American Journal of Mathematics by Samuel Eilenberg and Joseph A. Zilber. One possible route to a proof is the acyclic model theorem.
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| - Satz von Eilenberg-Zilber (de)
- Eilenberg–Zilber theorem (en)
- Théorème d'Eilenberg-Zilber (fr)
- 에일렌베르크-질버 사상 (ko)
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| - Der Satz von Eilenberg-Zilber, benannt nach S. Eilenberg und J. A. Zilber, ist ein Satz aus dem mathematischen Teilgebiet der algebraischen Topologie. Er stellt einer Verbindung zwischen den singulären Homologiegruppen eines kartesischen Produktes zweier topologischer Räume und Homologiegruppen der Räume selbst her. (de)
- In mathematics, specifically in algebraic topology, the Eilenberg–Zilber theorem is an important result in establishing the link between the homology groups of a product space and those of the spaces and . The theorem first appeared in a 1953 paper in the American Journal of Mathematics by Samuel Eilenberg and Joseph A. Zilber. One possible route to a proof is the acyclic model theorem. (en)
- En mathématiques, le théorème d'Eilenberg-Zilber est un résultat de topologie algébrique qui établit une équivalence d'homotopie entre le complexe de chaînes du produit de deux espaces et le produit tensoriel des complexes de chaînes de chacun d'eux. Le calcul de l'homologie de l'espace produit en fonction de celles des deux facteurs est ainsi réduit à un pur problème d'algèbre homologique, traité par le théorème de Künneth. (fr)
- 호몰로지 대수학에서 에일렌베르크-질버 사상(Eilenberg-Zilber寫像, 영어: Eilenberg–Zilber map)과 알렉산더-휘트니 사상(Alexander-Whitney寫像, 영어: Alexander–Whitney map)은 아벨 범주 위의 단체 대상의 텐서곱과 사슬 복합체의 텐서곱을 비교하는, 서로 반대 방향의 두 사슬 복합체 사상이다. 이들의 합성은 사슬 복합체의 호모토피를 이루어, 호몰로지 군의 동형을 유도한다. 즉, 단체 대상의 텐서곱과 사슬 복합체의 텐서곱은 같은 호몰로지 군을 정의한다. (ko)
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| - Der Satz von Eilenberg-Zilber, benannt nach S. Eilenberg und J. A. Zilber, ist ein Satz aus dem mathematischen Teilgebiet der algebraischen Topologie. Er stellt einer Verbindung zwischen den singulären Homologiegruppen eines kartesischen Produktes zweier topologischer Räume und Homologiegruppen der Räume selbst her. (de)
- In mathematics, specifically in algebraic topology, the Eilenberg–Zilber theorem is an important result in establishing the link between the homology groups of a product space and those of the spaces and . The theorem first appeared in a 1953 paper in the American Journal of Mathematics by Samuel Eilenberg and Joseph A. Zilber. One possible route to a proof is the acyclic model theorem. (en)
- En mathématiques, le théorème d'Eilenberg-Zilber est un résultat de topologie algébrique qui établit une équivalence d'homotopie entre le complexe de chaînes du produit de deux espaces et le produit tensoriel des complexes de chaînes de chacun d'eux. Le calcul de l'homologie de l'espace produit en fonction de celles des deux facteurs est ainsi réduit à un pur problème d'algèbre homologique, traité par le théorème de Künneth. (fr)
- 호몰로지 대수학에서 에일렌베르크-질버 사상(Eilenberg-Zilber寫像, 영어: Eilenberg–Zilber map)과 알렉산더-휘트니 사상(Alexander-Whitney寫像, 영어: Alexander–Whitney map)은 아벨 범주 위의 단체 대상의 텐서곱과 사슬 복합체의 텐서곱을 비교하는, 서로 반대 방향의 두 사슬 복합체 사상이다. 이들의 합성은 사슬 복합체의 호모토피를 이루어, 호몰로지 군의 동형을 유도한다. 즉, 단체 대상의 텐서곱과 사슬 복합체의 텐서곱은 같은 호몰로지 군을 정의한다. (ko)
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