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Constructing Path Connected Space

  1. Sep 19, 2010 #1
    1. The problem statement, all variables and given/known data

    1. Construct a path connected space X such that the fundamental group of (X,x_0)
    where x_0 is the base point; such that the fundamental group is the symmetric
    group on 3 letters?

    2. Let Z be the space obtained from a hollow cube by deleting the interior of its
    faces. Compute fundamental group of (Z,z_0) where z_0 is a basepoint.
    2. Relevant equations

    3. The attempt at a solution

    Both problems seem very related; I believe if I can solve one of them I can mostly like use similar ideas to solve the other. It seems like it must admit a simple solution; a graph of some sort. But I cannot spot any at the moment
  2. jcsd
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