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Let $Z * Z/2Z = \langle a, b | b^2=1\rangle$ be represented by $X = S^1\vee RP^2$ i.e. the wedge of the unit circle and the real projective plane.

Let $H$ be the smallest normal subgroup containing $b$.

Question:

How can we construct a covering space $\tilde X$ corresponding to $H$ by sketching a good picture for $\tilde X$ that covers X.

Any help is really appreciated.

Thanks

yaa09d
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    It's got to be a simply-connected space, consisting of a union of lines and 2-spheres. Every 2-sphere has to have two lines incident to it, and every line has to have a 2-sphere incident to it at every integral point. – Ryan Budney Jan 22 '12 at 00:12
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    Its not going to be simply connected, since it corresponds to $H$, as opposed to the trivial subgroup. But, Ryan Budney's idea is good. Just replace "sphere" with "$\mathbb R P^2$". – user15464 Jan 22 '12 at 00:52
  • Whoops, I thought he was asking for the universal cover. – Ryan Budney Jan 22 '12 at 01:15

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