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I am recently studying cellular homology but I am not very familiar with the CW complex. To compute the homology of $S^n\times S^n$, we can check the CW structure of $S^n\times S^n$ that has one $0$-cell, two $n$-cell, and one $2n$-cell. How do we derive this CW structure? I only know how to do for $S^1\times S^1$, that is, we can write down the labeling scheme for $S^1\times S^1$.

quuuuuin
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    In general, the product of two CW complexes can be equipped with a CW structure. Explicitly, the cells of $X \times Y$, are of the form $\alpha \times \beta$, where $\alpha$ is a cell of $X$ and $\beta$ is a cell of $Y$. You should be able to find details in Hatcher's Algebraic Topology. – Brian Shin Dec 09 '21 at 02:08
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    The accepted answer to this question addresses the more general question of finding a CW-structure on $A \times B$, where $A$ and $B$ are CW-complexes. – Sammy Black Dec 09 '21 at 02:09
  • Thanks for the help! – quuuuuin Dec 09 '21 at 02:18

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