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Fundamental Groups of the Mobius Band

  1. Dec 16, 2006 #1
    Seems to be isomorphic to Z, but I can't seem to be able to prove it.

    Am I right? If I am, how do I prove it?
     
  2. jcsd
  3. Dec 16, 2006 #2

    matt grime

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    It's homotopic to the circle.
     
  4. Dec 17, 2006 #3
    Sounds good. Just by shrinking?

    Maybe it's easier that I thought.
     
  5. Dec 17, 2006 #4

    matt grime

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    Or you could write down the universal cover and work out the group of deck transformations. Which is just as easy.
     
  6. Dec 19, 2006 #5
    You lost me there - don't know what a "universal cover" is.
     
  7. Dec 20, 2006 #6

    matt grime

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    You will soon. So just do it directly from the homotopy idea.
     
  8. Dec 20, 2006 #7
    Ok, thanks a lot.
     
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