Eilenberg–MacLane space

In mathematics, and algebraic topology in particular, an Eilenberg–MacLane space is a topological space with a single nontrivial homotopy group. As such, 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 constructions of spaces, computations of homotopy groups of spheres, and definition of cohomology operations. The name is for Samuel Eilenberg and Saunders Mac Lane, who introduced such spaces in the late 1940s.

Let G be a group and n a positive integer. A connected topological space X is called an Eilenberg–MacLane space of type K(G, n), if it has n-th homotopy group π_n(X) isomorphic to G and all other homotopy groups trivial. If n > 1 then G must be abelian. Such a space exists, is a CW-complex, and is unique up to a weak homotopy equivalence. By abuse of language, any such space is often called just K(G, n).

Examples

Kōzō

Kōzō, Kozo or Kouzou (written: 浩三, 公三, 公造, 航三, 恒三, 耕三, 耕造, 幸三, 光三, 興三, 更三, 孝蔵, 皐蔵, 弘三 or 弘蔵) is a masculine Japanese given name. Notable people with the name include:

KZ

KZ, K-Z, or kz may refer to:

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Koz

Koz or KOZ may refer to:

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