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May 25, 2022 at 7:34 comment added tota I have edited now @AleksandarMilivojević
May 25, 2022 at 7:32 history edited tota CC BY-SA 4.0
added 24 characters in body
May 25, 2022 at 7:30 comment added tota What if $F$ is homotopic to a covering space of $X$@RyanBudney?
May 25, 2022 at 7:13 comment added Ryan Budney Provided the fibers have the homotopy-type of a discrete space, your map has many of the properties of a covering map. And this is essentially an if and only if statement, via @SamNead's comment.
May 25, 2022 at 7:03 comment added Aleksandar Milivojević Just having finite fibers with an abstract biholomorphism of the fiber taking any given point to any other will surely not generally guarantee normality of the subgroup (your parenthetical remark); this biholomorphism should be the restriction of a deck transformation.
May 25, 2022 at 6:28 answer added Sam Nead timeline score: 2
May 25, 2022 at 6:03 history asked tota CC BY-SA 4.0