Math 527 - Homotopy Theory Eilenberg-MacLane spaces and cohomology
نویسنده
چکیده
Definition 1.2. Let n ≥ 1 and let G be an abelian group. The fundamental class of K(G, n) is the cohomology class ιn ∈ H (K(G, n);G) corresponding to idG via the isomorphism H n (K(G, n);G) ∼= HomZ(G,G). More explicitly, let ψ : πnK(G, n) ∼= −→ G be some chosen identification, and let h : πn (K(G, n)) ∼= −→ Hn (K(G, n);Z) denote the Hurewicz morphism, defined by h(α) = α∗(un), where un ∈ Hn(S) is a suitably chosen generator. Then ιn is defined by the equation 〈ιn, h(α)〉 = ψ(α)
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