Algebraic Topology · Problem 2.1.31

Homology — Allen Hatcher

Mathematics — Topology · five-lemma

Problem

Using the notation of the five-lemma, give an example where the maps α\alpha, β\beta, δ\delta, and ε\varepsilon are zero but γ\gamma is nonzero. This can be done with short exact sequences in which all the groups are either Z\mathbb{Z} or 00.

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