Let $G$ be an abelian group and $K_n=K(G,n)$ be the Eilenberg-Maclane space. How to obtain $K_m\wedge K_n$ is $(m+n-1)$-connected? (Hatcher's book page 404)
2026-03-25 23:44:01.1774482241
smash product of Eilenberg-Maclane spaces
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Construct $K(G, n)$ by starting with $n$-cells and then attaching cells of higher dimension to kill the homotopy groups above dimension $n$; do the same for $K(G, m)$. The smash product will then have no cells below dimension $n + m$.