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Covering spaces of S1 V S1

  1. Feb 16, 2010 #1
    1. The problem statement, all variables and given/known data

    Find all 3-fold covering spaces of S1 V S1 (the one-point union, or wedge sum, of two copies of the circle, S1).



    2. Relevant equations

    There is, as a hint, diagrams of the 3-fold covering spaces of the circle itself.



    3. The attempt at a solution

    Call the wedge sum W.

    One 3-fold covering space is W X {1, 2, 3}. This is just the space consisting of 3 disjoint copies of W. But this was pretty easy.

    I do not know how to construct the other covering spaces. Is there a way to use the covering spaces of the circle to construct covering spaces of W? Or at least a way to think about the covering space of the circle that could give me some insight? So far, I've only managed to stare at my sheet in a dazed fashion (other than the one covering space I did think of).
     
  2. jcsd
  3. Feb 16, 2010 #2
    I have six diagrams so far. Anybody know off-hand how many 3-fold covers of S1 V S1 there are or how one might determine how many there are?
     
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