Fundamental Groups of the Mobius Band

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?
 

matt grime

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It's homotopic to the circle.
 
Sounds good. Just by shrinking?

Maybe it's easier that I thought.
 

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.
 
You lost me there - don't know what a "universal cover" is.
 

matt grime

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You will soon. So just do it directly from the homotopy idea.
 
Ok, thanks a lot.
 

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