Can the fundamental group of some surface have more than one path homotopy class? Maybe this is a dumb question, but I'm really struggling with this
2026-04-04 17:51:58.1775325118
Question about the Fundamental Group as a notion
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Yes. The fundmental group of a torus is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}$ so has infinitely many homotopy classes.