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Apr 20, 2013 at 4:04 comment added Serge Lvovski @Misha: you bet it's positive in this case, when $\pi_1$ is commutative and generated by loops about components:) If I am not mistaken, the answer is also positive if $C_2$ has only normal crossings and each component of $C_2$ is transversal to $C_1$. I wonder what happens in general...
Apr 19, 2013 at 15:49 comment added Misha If $C_1\cup C_2$ has only normal crossings, the answer is positive; I am not sure otherwise.
Apr 18, 2013 at 17:19 history asked Serge Lvovski CC BY-SA 3.0