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enter image description here

The figure gives a 4-sheeted covering map from the torus to the Klein bottle. I am trying to show that this covering map is not normal, but I got stuck. (Actually I am solving an exercise to construct a non-normal covering of the Klein bottle by a torus.) Is there an efficient way to show that this covering is not normal?

Edit: Is this actually a covering map? If we let $a$ denote the loop on the Klein bottle given by the arrow $>>$, then I can't see it's lift starting at the corner point of the torus.

user302934
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Your map is not a cover, it is not locally injective near the horizontal edges. You can find a correct construction at Non-normal covering of a Klein bottle by torus.. In the comments there it is also noted that the minimum degree of such a map is $6$.

ronno
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