Fundamental Groups of the Mobius Band

1. Dec 16, 2006

Palindrom

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. Dec 16, 2006

matt grime

It's homotopic to the circle.

3. Dec 17, 2006

Palindrom

Sounds good. Just by shrinking?

Maybe it's easier that I thought.

4. Dec 17, 2006

matt grime

Or you could write down the universal cover and work out the group of deck transformations. Which is just as easy.

5. Dec 19, 2006

Palindrom

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

6. Dec 20, 2006

matt grime

You will soon. So just do it directly from the homotopy idea.

7. Dec 20, 2006

Palindrom

Ok, thanks a lot.