Define $S^3$ as $$ S^3 = \left\lbrace (z_1, z_2) \mid |z_1|^2 + |z_2|^2 = 2 \right\rbrace $$ and curve $C$ as $$ C(t) = (e^{imt}, e^{int}) $$ for $m,n \in \mathbb{Z}$, such that gcd(m,n) = 1. The task is to find $\pi_1(S^3 \setminus C).$ I know that I should use Seifert–van Kampen theorem here, but I don't know what to start with. May somebody suggest something?
2026-04-03 14:28:46.1775226526
Fundamental group of S_3 without curve
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