An Eilenberg-MacLane space is a fundamental concept in algebraic topology, named after mathematicians Samuel Eilenberg and Saunders Mac Lane. It is used to study topological properties related to cohomology theories and homotopy theory.
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A connected Eilenberg–MacLane space , , has and all other positive-degree homotopy groups trivial. The group must be abelian when , but may be nonabelian when . For an abelian group, the Dold–Kan correspondence constructs a simplicial model from the chain complex concentrated in degree . A classifying space of a discrete group gives the general case.