In mathematics, specifically algebraic topology, an Eilenberg–MacLane space is a topological space with a single nontrivial homotopy group. Let G be a...
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Eilenberg (1848–1927), German composer Eilenberg–MacLane space Eilenberg–Moore algebra Eilenberg–Steenrod axioms Eilenberg machine Eilenburg Eulenberg (disambiguation)...
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algebraic topology, there is a distinguished class of spectra called Eilenberg–Maclane spectra H A {\displaystyle HA} for any Abelian group A {\displaystyle...
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}} , which is contractible. The infinite projective space is therefore the Eilenberg–MacLane space K(Z2, 1). For each nonnegative integer q, the modulo...
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Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish-American mathematician who co-founded category theory (with Saunders Mac Lane) and...
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groups of X are trivial, that is, BG is an Eilenberg–MacLane space, or a K(G, 1). An example of a classifying space for the infinite cyclic group G is the...
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Samuel Eilenberg. Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftville. He was christened "Leslie Saunders MacLane", but...
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Cohomology (section Eilenberg–MacLane spaces)
Such a space is called an Eilenberg–MacLane space. This space has the remarkable property that it is a classifying space for cohomology: there is a natural...
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Homotopy category (redirect from Homotopy category of topological spaces)
and natural number i, there is a CW complex K(A,i ) called an Eilenberg–MacLane space and a cohomology class u in H i(K(A,i ),A) such that the resulting...
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group G has cohomological dimension 2, then it has a 2-dimensional Eilenberg–MacLane space K ( G , 1 ) {\displaystyle K(G,1)} . For n different from 2, a...
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