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Jan 25, 2010 at 8:58 comment added Ben Webster Mariano- you've given the criterion for the lifting to also take a chosen basepoint in the covering space to that basepoint. If you haven't made choices of basepoints, you should never have a criterion involving actual subgroups of $\pi_1$, since those aren't well-defined.
Jan 25, 2010 at 3:49 history edited Mariano Suárez-Álvarez CC BY-SA 2.5
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Jan 25, 2010 at 3:39 history edited Mariano Suárez-Álvarez CC BY-SA 2.5
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Jan 25, 2010 at 3:22 history answered Mariano Suárez-Álvarez CC BY-SA 2.5