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Feb 22, 2018 at 9:50 comment added Selim G Hi Richard thank you for the nice answer. I need to reformulate Q3 because that is not exactly what I had in mind: I meant embedding in a way which is $\pi_1$-injective because otherwise indeed you can play the game you suggested.
Feb 22, 2018 at 6:48 history edited Thomas Richard CC BY-SA 3.0
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Feb 21, 2018 at 12:32 history edited Thomas Richard CC BY-SA 3.0
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Feb 21, 2018 at 11:05 history answered Thomas Richard CC BY-SA 3.0