Let $T= \mathbb{S^1} \times \mathbb{S^1} $ denote the two dimensional torus and let $W = \mathbb{S^1} \vee \mathbb{S^1} $. I don't know how to show that $W$ is not a retract of $T$. Thanks for helping.
2026-05-02 10:17:27.1777717047
Retract of a torus.
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The fundamental group of the torus is $Z\oplus Z$ and the fundamental group of $W$ is the free group generated by two elements.