- Eilenberg-MacLane space
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Eilenberg-MacLane space
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Eilenberg-MacLane space — In mathematics, an Eilenberg MacLane space is a special kind of topological space that can be regarded as a building block for homotopy theory. These spaces are important in many contexts in algebraic topology, including stage by stage… … Wikipedia
Eilenberg — is a surname, and may refer to:* Samuel Eilenberg, Polish mathematician * Richard Eilenberg, German composer, see German article.;named after Samuel: * Eilenberg MacLane space * Eilenberg Moore algebra * Eilenberg Steenrod axioms See also *… … Wikipedia
Eilenberg-Ganea conjecture — The Eilenberg Ganea conjecture is a claim in algebraic topology. It was formulated by Samuel Eilenberg and Tudor Ganea in 1957, in a short, but influential paper. It states that if a group G has cohomological dimension 2, then it has a 2… … Wikipedia
Classifying space — 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 for which all its homotopy groups are trivial) by a free action of G. It… … Wikipedia
Samuel Eilenberg — Infobox Scientist box width = name = Samuel Eilenberg image size = caption = Samuel Eilenberg (1970) birth date = birth date|1913|9|30 birth place = Warsaw, Russian Empire death date = death date and age|1998|1|30|1913|9|30 death place =… … Wikipedia
Aspherical space — In topology, an aspherical space is a topological space with all higher homotopy groups equal to {0}. If one works with CW complexes, one can reformulate this condition: an aspherical CW complex is a CW complex whose universal cover is… … Wikipedia
Moore space (algebraic topology) — See also Moore space for other meanings in mathematics. In algebraic topology, a branch of mathematics, Moore space is the name given to a particular type of topological space that is the homology analogue of the Eilenberg–Maclane spaces of… … Wikipedia
List of cohomology theories — This is a list of some of the ordinary and generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW complexes or spectra. For other sorts of homology theories see the links at… … Wikipedia
Projective unitary group — In mathematics, the projective unitary group PU( n ) is the quotient of the unitary group U( n ) by the right multiplication of its center, U(1), embedded as scalars.Abstractly, it is the isometry group of complex projective space, just as the… … Wikipedia
Spectrum (homotopy theory) — In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. There are several different constructions of categories of spectra, all of which give the same homotopy category.Suppose we… … Wikipedia
