Algebraic Topology · Problem 2.2.15

Homology — Allen Hatcher

Mathematics — Topology · cellular-homology

Problem

Show that if XX is a CW complex then Hn(Xn)H_n(X^n) is free by identifying it with the kernel of the cellular boundary map Hn(Xn,Xn−1)→Hn−1(Xn−1,Xn−2)H_n(X^n, X^{n-1}) \to H_{n-1}(X^{n-1}, X^{n-2}).

Related theory

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