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The fundamental group of the complement of codimension 2 submanifold
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The fundamental group of the complement of codimension 2 submanifold
The condition is $f_*\colon \pi_1(M)\to \pi_1(V)$ is surjective not $\operatorname{inc}_*\colon \pi_1(V-f(M))\to \pi_1(V)$ is surjective.
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The fundamental group of the complement of codimension 2 submanifold