About: Eilenberg–MacLane space

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Eilenberg–MacLane space Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : dbpedia.org associated with source document(s)
QRcode icon

http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FEilenberg%E2%80%93MacLane_space

In mathematics, specifically algebraic topology, an Eilenberg–MacLane space is a topological space with a single nontrivial homotopy group. Let G be a group and n a positive integer. A connected topological space X is called an Eilenberg–MacLane space of type , if it has n-th homotopy group isomorphic to G and all other homotopy groups trivial. If then G must be abelian. Such a space exists, is a CW-complex, and is unique up to a weak homotopy equivalence, therefore any such space is often just called .

Attributes	Values
rdfs:label	Eilenberg-MacLane-Raum (de) Eilenberg–MacLane space (en) Espace d'Eilenberg-MacLane (fr) 에일렌베르크-매클레인 공간 (ko) K(G,n) пространство (ru)
rdfs:comment	대수적 위상수학에서 에일렌베르크-매클레인 공간(-空間, 영어: Eilenberg–MacLane space)은 주어진 특정 차수의 호모토피 군을 제외하고 다른 호모토피 군이 모두 자명군인 위상 공간이다. (ko) пространства (или пространства Эйленберга — Маклейна) — топологические пространства с единственной нетривиальной гомотопической группой в размерности . Названы в честь Сэмюэля Эйленберга и Сондерса Маклейна, которые рассматривали эти пространства в конце 1940-х годов. (ru) In mathematics, specifically algebraic topology, an Eilenberg–MacLane space is a topological space with a single nontrivial homotopy group. Let G be a group and n a positive integer. A connected topological space X is called an Eilenberg–MacLane space of type , if it has n-th homotopy group isomorphic to G and all other homotopy groups trivial. If then G must be abelian. Such a space exists, is a CW-complex, and is unique up to a weak homotopy equivalence, therefore any such space is often just called . (en) In der algebraischen Topologie, einem Teilgebiet der Mathematik, ist ein Eilenberg-MacLane Raum ein topologischer Raum mit einer einzigen nicht trivialen Homotopiegruppe. Für eine Gruppe G und eine positive natürliche Zahl heißt ein zusammenhängender topologischer Raum ein Eilenberg-MacLane Raum , falls die n-te Homotopiegruppe isomorph zu G ist und alle anderen Homotopiegruppen trivial sind. Der Name ist auf die Mathematiker Samuel Eilenberg und Saunders Mac Lane zurückzuführen, die solche Räume in den 1940er Jahren studierten. (de) En mathématiques, un espace d'Eilenberg-MacLane est un espace topologique ayant un seul groupe d'homotopie non trivial. Ce type d'espace joue un rôle de composant élémentaire en théorie de l'homotopie, puisqu'il jouit d'une forme d'unicité et intervient dans des procédés de reconstruction d'espaces plus complexes (il en est ainsi des tours de Postnikov). (fr)
dcterms:subject	Homotopy theory
Wikipage page ID	1073230 (xsd:integer)
Wikipage revision ID	1093922466 (xsd:integer)
Link from a Wikipage to another Wikipage	Product topology Samuel Eilenberg Saunders Mac Lane Moore space (algebraic topology) Braid group Algebraic topology Annals of Mathematics Unit circle Universal bundle Universal coefficient theorem Trivial group Compact space Mathematics Classifying space N-connected space Configuration space (mathematics) Connected space Contractible space Short exact sequence Simplicial abelian group String theory Complex projective space Empty set Fundamental class Fundamental group Leray spectral sequence Spectrum (topology) Spin group String group Symmetric product (topology) Wedge sum Topological group Torus Cyclic group Brown's representability theorem Christos Papakyriakopoulos Direct limit Lens space Postnikov system Homotopy theory Group (mathematics) Group cohomology J. Peter May Jean-Pierre Serre Covering space Stable homotopy theory Abelian group Cohomology Cohomology operation Homotopy group Homotopy theory Aspherical space Manifold Sphere Fibration Free group Group isomorphism Groupoid Integer Cartan–Hadamard theorem Category theory Real projective space Loop space Steenrod algebra Non-positive curvature Yoneda lemma Serre spectral sequence Space (mathematics) Brown representability theorem Fivebrane group Representing space Whitehead tower Higher group Singular cohomology Postnikov tower CW-complex Weak homotopy equivalence dbr:Arxiv:1312.5676
Link from a Wikipage to an external page	http://doc.rero.ch/record/482/files/Clement_these.pdf http://www.numdam.org/volume/SHC_1954-1955__7/ https://www.jstor.org/stable/1969849%7Cjournal= https://mathoverflow.net/questions/24754/cohomology-of-the-eilenberg-maclane-spaces-kg-n https://encyclopediaofmath.org/wiki/Eilenberg-MacLane_space
sameAs	Eilenberg–MacLane space Eilenberg–MacLane space Eilenberg–MacLane space Eilenberg–MacLane space

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (61 GB total memory, 43 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software