Algebraic Topology · Problem 3F.8

Cohomology — Allen Hatcher

Mathematics — Topology · bockstein-moore-space-ext

Problem

Show that for a Moore space M(G,n)M(G, n) the Bockstein long exact sequence in cohomology associated to the short exact sequence of coefficient groups 0→A→B→C→00 \to A \to B \to C \to 0 reduces to an exact sequence 0→Hom(G,A)→Hom(G,B)→Hom(G,C)→Ext(G,A)→Ext(G,B)→Ext(G,C)→00 \to \mathrm{Hom}(G, A) \to \mathrm{Hom}(G, B) \to \mathrm{Hom}(G, C) \to \mathrm{Ext}(G, A) \to \mathrm{Ext}(G, B) \to \mathrm{Ext}(G, C) \to 0

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