Ok so apparently the universal cover of the figure-8 can be represented by the cayley graph of the free group on two generators, discussed in Hatcher and here http://en.wikipedia.org/wiki/Rose_%28topology%29" [Broken](adsbygoogle = window.adsbygoogle || []).push({});

i can see why this is a universal cover of the figure-8. but I'm having trouble understanding why it cannot be something more simple.

for example, create a graph with one central vertex, and then four vertices surrounding it, and then connect each vertex to only the central vertex. (so you get a plus sign with vertices on the tips and one in the middle). isn't there a correct labeling on the edges of this graph to be a cover of the figure-8?

I'm not sure if this graph would be homeomorphic to the Cayley graph...ugh fractals.

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# Universal cover of figure-8

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