Hey I am having a little bit of difficulty.(adsbygoogle = window.adsbygoogle || []).push({});

The classification theorem for 2 - manifolds tells me that every 2 -manifold has the following representation:

1) connect sum of n-tori

2) connect sum of n-projective planes

3) a sphere

Now, using Massey's book there is a very algorithmic way to take a polygon given its edge representation (say aa*bc*d*bcd*, something like that) and get to one of those forms.

But such a simple example, the Mobius strip, I get lost on and I'm not sure how to realize it.

When I think of the Mobius strip as a CW complex, I envision the 1 skeleton as a square with 3 1-cells connected to 2 0-cells, and a 2 cell as the middle of the "square", so the following edge orientation: aba*d. How do I realize this as a connect sum of tori, or projective planes? Massey's algorithm only seems to work when edges are paired up, so just having the one "b" and the one "d" means it doesn't work

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# Fundamental polygon of a Mobius strip

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