Definition 3.3.11 (Cellular homology). The cellular homology groups of an anima \(X\) with CW-structure are the homology groups of the cellular chain complex: \[ H_n^{\mathrm {CW}}(X) \;:=\; H_n(C_*^{\mathrm {CW}}(X)) \;=\; \ker (d_n) / \im (d_{n+1}). \]
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